1D Cadet Flight Manual

Predict, calculate with units, observe, and explain. Keep your first answer when you retry. The printable PDF includes the worksheet diagrams and calculation spaces.

G.U.E.S.S.: Givens, Unknowns, Equation, Substitute, Solve. The work boxes group G/U and S/S to match the 2D worksheets. Include units and signs; use slope or area relationships for graph calculations. Answer conceptual prompts in the explanation space.

Equations and notation

Use SI units and a stated positive direction. Displacement is final coordinate minus initial coordinate. The symbol t is an elapsed time interval; a bar over v indicates an average.

NYSED: d = x_f − x_i
AP: Δx = x − x₀
Displacement is the change in coordinate, with direction.

NYSED: v̄ = d / t
AP: v̄_x = Δx / Δt
Average speed uses total distance divided by elapsed time.

NYSED: a = (v_f − v_i) / t
AP: a_x = (v_x − v_x0) / t
This gives average acceleration; it equals a when acceleration is constant.

NYSED: v_f = v_i + at
AP: v_x = v_x0 + a_x t
Constant acceleration over this time interval.

NYSED: d = v_i t + ½at2
AP: x = x₀ + v_x0 t + ½a_x t2
Constant acceleration. Add the initial coordinate to displacement to find position.

NYSED: v̄ = (v_f + v_i) / 2; d = v̄t
AP: v̄_x = (v_x + v_x0) / 2; Δx = v̄_x t
Endpoint averaging applies to constant acceleration, not an arbitrary multi-stage trip.

NYSED: v_f2 = v_i2 + 2ad
AP: v_x2 = v_x02 + 2a_x(x − x₀)
Constant acceleration. Recover the sign of velocity from the physical direction.

NYSED: slope x-t to v; slope v-t to a; area v-t to d; area a-t to Δv
AP: slope x-t to v_x; slope v_x-t to a_x; area v_x-t to Δx; area a_x-t to Δv_x
Use signed area for displacement; add absolute area contributions for distance.

The core course contains K00-K21, followed by the guided 2D bridge T00-T02. A01-A05 and P01-P03 are optional AP Physics 1 extensions. Keep your first prediction when you retry. Your instructor reviews written reasoning separately from numerical results.

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

K00 / CORE

Your first displacement

A craft starts at x = -20 m and finishes at x = +20 m. Positive x points right. Predict its displacement, then observe the prescribed flight.

Initial position: -20 m
Final position: 20 m

G.U.E.S.S. / worked calculation

G / U: Use the givens above. Find signed displacement.

E: d = x_f - x_i

S / S: Substitute and solve with units.

Final position minus initial position: 20 - (-20) = +40 m.

The craft moves 40 m in the positive direction. A negative starting coordinate does not mean negative displacement.

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Signed displacement: __________________ m

Observe and explain

Open K00 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

If both coordinates increased by 100 m, would displacement change? Explain.

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

K01 / CORE

Across the origin

Move from x = -30 m to x = +20 m on the marked lane. Find the signed change in position.

Initial position: -30 m
Final position: 20 m

Guidance: Write final coordinate minus initial coordinate. Subtracting a negative adds its magnitude.

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Signed displacement: __________________ m

G.U.E.S.S. / flight calculation

1D calculation

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

Observe and explain

Open K01 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

Why is the final coordinate alone not the displacement?

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

K02 / CORE

Port-side transfer

The craft starts at x = +40 m and ends at x = -20 m. Find its displacement.

Initial position: 40 m
Final position: -20 m

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Signed displacement: __________________ m

G.U.E.S.S. / flight calculation

1D calculation

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

Observe and explain

Open K02 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

Does the negative sign describe a position, a direction of change, or both in this problem?

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

K03 / CORE

Return to the same marker

The prescribed route goes from x = 10 m to x = 19 m, then returns to x = 10 m. Find net displacement and total distance.

Start: 10 m
Turning position: 19 m
Finish: 10 m

G.U.E.S.S. / worked calculation

G / U: Use the givens above. Find net displacement; total distance.

E: d = x_f - x_i; distance = sum of the lengths of both legs

S / S: Substitute and solve with units.

Net displacement: 10 - 10 = 0 m.

Outward leg: 19 - 10 = 9 m. Return leg: 9 m. Total distance: 9 + 9 = 18 m.

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Net displacement: __________________ m

Total distance: __________________ m

Observe and explain

Open K03 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

How can the craft travel while its net displacement is zero?

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

K04 / CORE

Count both legs

The craft travels from x = -10 m to x = +6 m, then back to x = -10 m. Calculate displacement and distance.

Start: -10 m
Turning position: 6 m
Finish: -10 m

Guidance: Use only the first and last coordinates for displacement. Add the lengths of both legs for distance.

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Net displacement: __________________ m

Total distance: __________________ m

G.U.E.S.S. / flight calculation

1D calculation

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

Observe and explain

Open K04 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

Explain why total distance cannot be negative.

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

K05 / CORE

Read the position trace

The craft moves from x = 10 m to x = 40 m in 6 s at constant velocity. Find its average velocity.

Initial position: 10 m
Final position: 40 m
Elapsed time: 6 s

Given graph data

Position (m)

Time (s)	Value
0	10
0.75	13.75
1.5	17.5
2.25	21.25
3	25
3.75	28.75
4.5	32.5
5.25	36.25
6	40

G.U.E.S.S. / worked calculation

G / U: Use the givens above. Find average velocity.

E: d = x_f - x_i; average velocity = d / t

S / S: Substitute and solve with units.

Displacement: 40 - 10 = 30 m.

Average velocity: 30 / 6 = +5 m/s. The position-time slope gives the same result.

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Average velocity: __________________ m/s

Observe and explain

Open K05 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

Why is the slope 5 m/s even though the graph starts at 10 m?

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

K06 / CORE

A descending position trace

Use the position-time graph to find the craft's average velocity and average speed from 0 to 5 s.

Initial position: 40 m
Elapsed time: 5 s

Given graph data

Position (m)

Time (s)	Value
0	40
0.625	36.25
1.25	32.5
1.875	28.75
2.5	25
3.125	21.25
3.75	17.5
4.375	13.75
5	10

Guidance: Slope is change in position divided by change in time. Read both endpoints.

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Average velocity: __________________ m/s

Average speed: __________________ m/s

G.U.E.S.S. / flight calculation

1D calculation

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

Observe and explain

Open K06 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

Does a downward-sloping position graph mean that speed is decreasing?

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

K07 / CORE

Find the travel time

A craft coasts from x = -10 m to x = +30 m at +8 m/s. How much time does the trip take?

Initial position: -10 m
Final position: 30 m
Constant velocity: 8 m/s

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Elapsed time: __________________ s

G.U.E.S.S. / flight calculation

1D calculation

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

Observe and explain

Open K07 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

Show how you rearranged the average-velocity equation to isolate time.

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

K08 / CORE

Changing velocity

The craft's velocity changes uniformly from +2 m/s to +14 m/s in 4 s. Find its acceleration.

Initial velocity: 2 m/s
Final velocity: 14 m/s
Elapsed time: 4 s

Given graph data

Velocity (m/s)

Time (s)	Value
0	2
0.5	3.5
1	5
1.5	6.5
2	8
2.5	9.5
3	11
3.5	12.5
4	14

G.U.E.S.S. / worked calculation

G / U: Use the givens above. Find acceleration.

E: a = (v_f - v_i) / t

S / S: Substitute and solve with units.

Change in velocity: 14 - 2 = 12 m/s.

Acceleration: 12 / 4 = +3 m/s2. The velocity-time slope is positive.

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Acceleration: __________________ m/s²

Observe and explain

Open K08 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

What does +3 m/s² mean about each second of this motion?

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

K09 / CORE

Negative acceleration and speed

A craft already moving left at -4 m/s accelerates at -2 m/s² for 3 s. Predict its final velocity and change in speed.

Initial velocity: -4 m/s
Constant acceleration: -2 m/s²
Elapsed time: 3 s

Guidance: Add acceleration multiplied by time to the initial velocity. Compare velocity magnitudes for speed.

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Final velocity: __________________ m/s

During this interval, the craft's speed...

increases
decreases
stays constant

G.U.E.S.S. / flight calculation

1D calculation

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

Observe and explain

Open K09 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

Compare your first prediction with the observed motion. Explain any correction using an equation or graph.

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

K10 / CORE

Brake to rest

A craft moving at +12 m/s slows uniformly to rest in 4 s. Determine its acceleration.

Initial velocity: 12 m/s
Final velocity: 0 m/s
Elapsed time: 4 s

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Acceleration: __________________ m/s²

G.U.E.S.S. / flight calculation

1D calculation

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

Observe and explain

Open K10 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

Why is acceleration negative here? Would a negative acceleration always slow a craft?

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

K11 / CORE

Travel while accelerating

A craft starts at x = -10 m with velocity +3 m/s. It accelerates at +2 m/s² for 4 s. Find its displacement and final position.

Initial position: -10 m
Initial velocity: 3 m/s
Constant acceleration: 2 m/s²
Elapsed time: 4 s

G.U.E.S.S. / worked calculation

G / U: Use the givens above. Find displacement; final position.

E: d = v_i t + (1/2)at2; x_f = x_i + d

S / S: Substitute and solve with units.

Displacement: (3)(4) + (1/2)(2)(42) = 12 + 16 = 28 m.

Final position: -10 + 28 = 18 m.

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Displacement: __________________ m

Final position: __________________ m

Observe and explain

Open K11 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

What contribution comes from initial velocity, and what contribution comes from acceleration?

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

K12 / CORE

Average the endpoints

Velocity increases uniformly from +4 m/s to +16 m/s in 6 s. Find average velocity and displacement.

Initial velocity: 4 m/s
Final velocity: 16 m/s
Elapsed time: 6 s

Given graph data

Velocity (m/s)

Time (s)	Value
0	4
0.75	5.5
1.5	7
2.25	8.5
3	10
3.75	11.5
4.5	13
5.25	14.5
6	16

Guidance: Average the two velocities, then multiply by elapsed time. Confirm using the trapezoid area on the velocity-time graph.

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Average velocity: __________________ m/s

Displacement: __________________ m

G.U.E.S.S. / flight calculation

1D calculation

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

Observe and explain

Open K12 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

Why must the acceleration be constant for this endpoint-average method?

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

K13 / CORE

A moving start

A craft begins at x = 10 m with velocity -2 m/s. Its constant acceleration is +3 m/s² for 4 s. Find displacement and final position.

Initial position: 10 m
Initial velocity: -2 m/s
Constant acceleration: 3 m/s²
Elapsed time: 4 s

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Displacement: __________________ m

Final position: __________________ m

G.U.E.S.S. / flight calculation

1D calculation

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

Observe and explain

Open K13 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

The craft initially moves left. Explain how its final displacement can be positive.

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

K14 / CORE

Stop without knowing time

A craft moving at +10 m/s brakes at a constant -2 m/s² until it stops. Find its stopping displacement using an equation without time.

Initial velocity: 10 m/s
Final velocity: 0 m/s
Constant acceleration: -2 m/s²

G.U.E.S.S. / worked calculation

G / U: Use the givens above. Find stopping displacement.

E: v_f2 = v_i2 + 2ad; d = (v_f2 - v_i2) / (2a)

S / S: Substitute and solve with units.

Use v_f2 = v_i2 + 2ad.

0 = 100 + 2(-2)d, so d = (0 - 100)/(-4) = +25 m.

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Stopping displacement: __________________ m

Observe and explain

Open K14 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

How do the signs of the numerator and denominator give a positive stopping displacement?

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

K15 / CORE

Stopping clearance

A craft moving at +8 m/s brakes at -2 m/s² to rest. Find the displacement needed to stop.

Initial velocity: 8 m/s
Final velocity: 0 m/s
Constant acceleration: -2 m/s²

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Stopping displacement: __________________ m

G.U.E.S.S. / flight calculation

1D calculation

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

Observe and explain

Open K15 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

Explain why using only initial velocity multiplied by time would be incorrect during braking.

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

K16 / CORE

Recover the direction

Initial velocity is -4 m/s. Constant acceleration is -2 m/s². After a displacement of -12 m, find the final velocity.

Initial velocity: -4 m/s
Constant acceleration: -2 m/s²
Displacement: -12 m

Guidance: First solve for the square of velocity. Use the direction of motion to choose the sign of its square root.

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Final velocity: __________________ m/s

G.U.E.S.S. / flight calculation

1D calculation

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

Observe and explain

Open K16 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

Why does taking only the positive square root give the wrong velocity?

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

K17 / CORE

Read a reversal

Use the velocity-time graph for this 6 s flight. Find displacement, distance, average velocity, and average speed, taking account of the reversal.

Initial position: 10 m
Elapsed time: 6 s

Given graph data

Velocity (m/s)

Time (s)	Value
0	6
0.75	4.5
1.5	3
2.25	1.5
3	0
3.75	-1.5
4.5	-3
5.25	-4.5
6	-6

G.U.E.S.S. / worked calculation

G / U: Use the givens above. Find displacement; total distance; average speed; average velocity.

E: triangle area = (1/2)(base)(height); d = signed area; distance = sum of area magnitudes; average velocity = d / t; average speed = distance / t

S / S: Substitute and solve with units.

Positive triangular area: (1/2)(3)(6) = +9 m.

Negative triangular area: -9 m. Displacement: 9 - 9 = 0 m.

Distance: 9 + 9 = 18 m. The reversal occurs when velocity crosses zero.

Average velocity: 0 / 6 = 0 m/s. Average speed: 18 / 6 = 3 m/s.

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Displacement: __________________ m

Total distance: __________________ m

Average speed: __________________ m/s

Average velocity: __________________ m/s

Observe and explain

Open K17 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

Which instant is the turning point, and what is the acceleration at that instant?

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

K18 / CORE

From acceleration to position

The acceleration-time graph is given. Initial velocity is -2 m/s. Find final velocity, displacement, and average speed after 4 s.

Initial velocity: -2 m/s
Elapsed time: 4 s

Given graph data

Acceleration (m/s²)

Time (s)	Value
0	1
4	1

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Final velocity: __________________ m/s

Displacement: __________________ m

Average speed: __________________ m/s

G.U.E.S.S. / flight calculation

1D calculation

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

Observe and explain

Open K18 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

Why is acceleration-time area a change in velocity rather than displacement?

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

K19 / CORE

Accelerate coast and brake

Use the supplied motion traces. The craft accelerates for 3 s, coasts for 2 s, then brakes for 3 s. Find total displacement and final velocity.

Initial velocity: 0 m/s
Total elapsed time: 8 s

Given graph data

Position (m)

Time (s)	Value
0	0
1	1
2	4
3	9
4	15
5	21
6	26
7	29
8	30

Velocity (m/s)

Time (s)	Value
0	0
1	2
2	4
3	6
4	6
5	6
6	4
7	2
8	0

Acceleration (m/s²)

Time (s)	Value
0	2
3	2
3	0
5	0
5	-2
8	-2

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Total displacement: __________________ m

Final velocity: __________________ m/s

During the middle interval, zero acceleration means...

the craft keeps its velocity
the craft must be at rest
its position resets to zero

G.U.E.S.S. / flight calculation

1D calculation

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

Observe and explain

Open K19 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

Calculate each interval separately. What carries over at the interval boundaries?

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

K20 / CORE

One dimension can be vertical

In an Earth-surface test chamber, a marker is released from y = 20 m. Positive y is upward. Ignore air resistance and use g = 9.8 m/s². Find its displacement and height after 2 s.

Initial height: 20 m
Initial velocity: 0 m/s
Vertical acceleration: -9.8 m/s²
Elapsed time: 2 s

G.U.E.S.S. / worked calculation

G / U: Use the givens above. Find vertical displacement; final height.

E: d_y = v_iy t + (1/2)a_y t2; y_f = y_i + d_y

S / S: Substitute and solve with units.

Vertical displacement: 0(2) + (1/2)(-9.8)(22) = -19.6 m.

Final height: 20 - 19.6 = 0.4 m.

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Vertical displacement: __________________ m

Final height: __________________ m

Observe and explain

Open K20 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

Why is acceleration negative when g itself is a positive magnitude?

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

K21 / CORE

Up and back

In the Earth-surface chamber, a marker starts at y = 10 m moving upward at +9.8 m/s. Use constant acceleration -9.8 m/s² and ignore air resistance. Find displacement and final velocity after 2 s.

Initial height: 10 m
Initial velocity: 9.8 m/s
Vertical acceleration: -9.8 m/s²
Elapsed time: 2 s

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Vertical displacement: __________________ m

Final vertical velocity: __________________ m/s

At the highest point, acceleration is...

-9.8 m/s²
zero
+9.8 m/s²

G.U.E.S.S. / flight calculation

1D calculation

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

Observe and explain

Open K21 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

Compare your first prediction with the observed motion. Explain any correction using an equation or graph.

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

T00 / CORE

Two axes one clock

Repeat the familiar horizontal flight while the craft also coasts vertically. Solve each component separately using the same 4 s. Then combine the components.

Initial x: -10 m
Initial y: 5 m
Initial horizontal velocity: 3 m/s
Initial vertical velocity: 1 m/s
Horizontal acceleration: 2 m/s²
Vertical acceleration: 0 m/s²
Shared elapsed time: 4 s

G.U.E.S.S. / worked calculation

G / U: Use the givens above. Find horizontal displacement; vertical displacement; final x coordinate; final y coordinate.

E: d_x = v_ix t + (1/2)a_x t2; d_y = v_iy t + (1/2)a_y t2; x_f = x_i + d_x; y_f = y_i + d_y

S / S: Substitute and solve with units.

Horizontal: d_x = 3(4) + (1/2)(2)(42) = 28 m. Final x = -10 + 28 = 18 m.

Vertical: d_y = 1(4) + (1/2)(0)(42) = 4 m. Final y = 5 + 4 = 9 m.

Displacement is (28, 4) m. Final position is (18, 9) m. Both components act during the same 4 s.

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Horizontal displacement: __________________ m

Vertical displacement: __________________ m

Final x coordinate: __________________ m

Final y coordinate: __________________ m

Observe and explain

Open T00 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

Why do the components share time even though their accelerations are different?

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

T01 / CORE

Coasting on two axes

The craft starts at (20, -10) m and coasts with velocity (-5, 3) m/s for 4 s. Find both displacement components and its final coordinates.

Initial x: 20 m
Initial y: -10 m
Horizontal velocity: -5 m/s
Vertical velocity: 3 m/s
Horizontal acceleration: 0 m/s²
Vertical acceleration: 0 m/s²
Shared elapsed time: 4 s

Guidance: Multiply each velocity component by the shared time. Add each displacement to its own starting coordinate.

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Horizontal displacement: __________________ m

Vertical displacement: __________________ m

Final x coordinate: __________________ m

Final y coordinate: __________________ m

G.U.E.S.S. / flight calculation

Both axes use one shared elapsed time.

HORIZONTAL / x

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

VERTICAL / y

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

Observe and explain

Open T01 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

Compare your first prediction with the observed motion. Explain any correction using an equation or graph.

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

T02 / CORE

Independent component check

A craft begins at (5, 10) m with velocity (2, -1) m/s. Constant acceleration is (1, 2) m/s² for 3 s. Find displacement and final velocity components.

Initial x: 5 m
Initial y: 10 m
Initial horizontal velocity: 2 m/s
Initial vertical velocity: -1 m/s
Horizontal acceleration: 1 m/s²
Vertical acceleration: 2 m/s²
Shared elapsed time: 3 s

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Horizontal displacement: __________________ m

Vertical displacement: __________________ m

Final horizontal velocity: __________________ m/s

Final vertical velocity: __________________ m/s

G.U.E.S.S. / flight calculation

Both axes use one shared elapsed time.

HORIZONTAL / x

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

VERTICAL / y

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

Observe and explain

Open T02 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

Explain which quantities belong to each axis and which quantity is shared.

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

A01 / AP PHYSICS 1

Stopping distance scales

Compare two stopping flights with the same braking acceleration magnitude. The second craft has twice the initial speed. Derive the stopping-distance factor, then calculate the second craft's stopping displacement.

Second initial velocity: 20 m/s
Final velocity: 0 m/s
Braking acceleration: -5 m/s²

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Stopping-distance factor: __________________

Second stopping displacement: __________________ m

G.U.E.S.S. / flight calculation

1D calculation

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

Observe and explain

Open A01 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

Derive d in terms of initial speed and braking acceleration magnitude before substituting. State what is held constant.

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

A02 / AP PHYSICS 1

Catch the courier

A pursuit craft starts at x = 0 from rest with constant acceleration +4 m/s². At the same instant, a courier is at x = 24 m coasting at +2 m/s. Find the positive meeting time and coordinate.

Pursuer initial position: 0 m
Pursuer initial velocity: 0 m/s
Pursuer acceleration: 4 m/s²
Courier initial position: 24 m
Courier velocity: 2 m/s

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Meeting time: __________________ s

Meeting coordinate: __________________ m

G.U.E.S.S. / flight calculation

1D calculation

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

Observe and explain

Open A02 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

Set the two position expressions equal. Explain why one algebraic time solution is not part of this flight.

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

A03 / AP PHYSICS 1

A delayed departure

The craft waits at rest for 2 s, then accelerates from rest at +2 m/s² for 4 s. Find its displacement and average velocity over the entire 6 s observation.

Waiting interval: 2 s
Acceleration interval: 4 s
Acceleration after waiting: 2 m/s²
Initial velocity: 0 m/s

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Total displacement: __________________ m

Average velocity over 6 s: __________________ m/s

G.U.E.S.S. / flight calculation

1D calculation

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

Observe and explain

Open A03 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

Why does the acceleration calculation use 4 s while average velocity uses 6 s?

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

A04 / AP PHYSICS 1

Measure acceleration

These simulated velocity measurements include small reading variations. Estimate acceleration using the first and last points, then choose a useful experimental graph. Write a procedure and discuss uncertainty in your manual.

Given graph data

Measured velocity (m/s)

Time (s)	Value
0	2
1	4.1
2	6
3	8.1
4	10

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Estimated acceleration: __________________ m/s²

To estimate constant acceleration from all the measurements, plot...

velocity against time and fit the slope
position against time and read the intercept
velocity against time and use its total area

G.U.E.S.S. / flight calculation

1D calculation

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

Observe and explain

Open A04 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

Describe how to collect independent position/time data, estimate velocities, and reduce timing uncertainty. What would curvature in the velocity-time graph suggest?

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

A05 / AP PHYSICS 1

Change the observer

In the map frame, a marker moves at +12 m/s and an observer coasts at +5 m/s. Find the marker's velocity relative to the observer.

Marker map velocity: 12 m/s
Observer map velocity: 5 m/s

Guidance: Subtract the observer's map velocity from the marker's map velocity.

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Velocity relative to observer: __________________ m/s

G.U.E.S.S. / flight calculation

1D calculation

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

Observe and explain

Open A05 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

Describe what the observer measures. Why do both inertial observers agree that the acceleration is zero?

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

P01 / AP PHYSICS 1

Resolve a velocity vector

A craft coasts at speed 20 m/s at 53.13° above +x. Use cos(53.13°) = 0.60 and sin(53.13°) = 0.80. Find the velocity components and displacements after 2 s.

Speed: 20 m/s
Angle above +x: 53.13 degrees
Shared elapsed time: 2 s

Guidance: Horizontal component = speed × cosine. Vertical component = speed × sine. Use the same elapsed time for both.

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Horizontal velocity: __________________ m/s

Vertical velocity: __________________ m/s

Horizontal displacement: __________________ m

Vertical displacement: __________________ m

G.U.E.S.S. / flight calculation

Both axes use one shared elapsed time.

HORIZONTAL / x

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

VERTICAL / y

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

Observe and explain

Open P01 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

Reconstruct the speed from the two velocity components. What changes if only the launch angle changes?

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

P02 / AP PHYSICS 1

Horizontal launch

In an Earth-surface chamber, a marker is launched horizontally at 15 m/s from height 19.6 m. Ground level is y = 0. Ignore air resistance and use g = 9.8 m/s². Find landing time, horizontal range, and final vertical velocity.

Initial height: 19.6 m
Landing height: 0 m
Horizontal velocity: 15 m/s
Initial vertical velocity: 0 m/s
Horizontal acceleration: 0 m/s²
Vertical acceleration: -9.8 m/s²

Guidance: Use the vertical displacement to solve for positive flight time. Reuse that time in the horizontal equation.

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Landing time: __________________ s

Horizontal range: __________________ m

Final vertical velocity: __________________ m/s

G.U.E.S.S. / flight calculation

Both axes use one shared elapsed time.

HORIZONTAL / x

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

VERTICAL / y

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

Observe and explain

Open P02 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

If the horizontal launch speed doubles, what happens to landing time and range? State your assumptions.

FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS

P03 / AP PHYSICS 1

Launch to a lower platform

A marker launches from (0, 14.7) m with velocity (12, 9.8) m/s and lands at y = 0. Ignore air resistance and use g = 9.8 m/s² downward. Find the positive flight time, horizontal range, and final vertical velocity.

Initial height: 14.7 m
Landing height: 0 m
Horizontal velocity: 12 m/s
Initial vertical velocity: 9.8 m/s
Horizontal acceleration: 0 m/s²
Vertical acceleration: -9.8 m/s²

Before observation: Predict the sign or direction before calculating. Explain your choice on paper.

Landing time: __________________ s

Horizontal range: __________________ m

Final vertical velocity: __________________ m/s

G.U.E.S.S. / flight calculation

Both axes use one shared elapsed time.

HORIZONTAL / x

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

VERTICAL / y

G / U Givens and unknowns

E Equation before substitution

S / S Substitute and solve with units

Observe and explain

Open P03 in the Academy. Enter your prediction, then observe. Keep your first answer visible.

Observed result: ____________________ Verified / Retry

Explain why the equal-height range formula is not suitable. Design a measurement that could check your predicted range.