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 = xf − xi AP: Δx = x − x0 Displacement is the change in coordinate, with direction.
NYSED: v̄ = d / t AP: v̄x = Δx / Δt Average speed uses total distance divided by elapsed time.
NYSED: a = (vf − vi) / t AP: ax = (vx − vx0) / t This gives average acceleration; it equals a when acceleration is constant.
NYSED: vf = vi + at AP: vx = vx0 + ax t Constant acceleration over this time interval.
NYSED: d = vi t + ½at2 AP: x = x0 + vx0 t + ½ax t2 Constant acceleration. Add the initial coordinate to displacement to find position.
NYSED: v̄ = (vf + vi) / 2; d = v̄t AP: v̄x = (vx + vx0) / 2; Δx = v̄x t Endpoint averaging applies to constant acceleration, not an arbitrary multi-stage trip.
NYSED: vf2 = vi2 + 2ad AP: vx2 = vx02 + 2ax(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 vx; slope vx-t to ax; area vx-t to Δx; area ax-t to Δvx 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 = xf - xi
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.
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: dy = viy t + (1/2)ay t2; yf = yi + dy
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.
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.
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: dx = vix t + (1/2)ax t2; dy = viy t + (1/2)ay t2; xf = xi + dx; yf = yi + dy
S / S: Substitute and solve with units.
Horizontal: dx = 3(4) + (1/2)(2)(42) = 28 m. Final x = -10 + 28 = 18 m.
Vertical: dy = 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.
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.
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.
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.
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.
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.
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.
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.
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.
FIRST LIGHT ACADEMY / HELIOS PROVING GROUNDS