A College Board-style free-response question on Unit 1: Kinematics. Work through each part, then reveal the model answer to see exactly what earns each point.
Scenario: A small ball is launched from the top of a 20 m tall cliff with an initial velocity of 15 m/s directed at an angle of 53° above the horizontal. The ball lands on the level ground at the base of the cliff. Air resistance is negligible. Use g = 10 m/s², sin 53° ≈ 0.80, and cos 53° ≈ 0.60.
— AP Physics 1 style problem · Topics 1.3 & 1.5
A
Calculate the horizontal and vertical components of the ball's initial velocity.
✓ Model answer (earns the points)
Resolve the initial velocity vector into perpendicular components:
Why it scores: Uses the correct trig functions (cos for x-component when angle is measured from the horizontal, sin for y-component). Shows numerical values with units. Naming directions (horizontal/upward) is good practice but optional.
B
Calculate the time the ball is in the air before it hits the ground at the base of the cliff.
✓ Model answer (earns the points)
Use vertical motion only. Take upward as positive, with the launch point as y = 0. The ground is then at y = −20 m. Vertical acceleration = −g = −10 m/s².
Take the positive root: t ≈ 3.53 s (the negative root is unphysical — it would be a time before launch).
Why it scores: Uses only the vertical motion (since the question is about time aloft). Correctly sets up signs (downward landing position is negative when up is positive). Solves the quadratic and rejects the negative root. Reports a reasonable physical answer with units.
C
A student claims, "Because the ball is launched upward and lands lower than it started, its average vertical velocity over the entire flight must be zero." Is the student correct? Justify your answer using a physical or mathematical argument.
✓ Model answer (earns the points)
The student is incorrect. Average vertical velocity equals the total vertical displacement divided by the total time: v_avg = Δy / Δt. The ball starts at the top of the cliff and lands 20 m below the launch point, so its vertical displacement is −20 m (not zero). Dividing by the total time of ~3.5 s gives an average vertical velocity of about −5.7 m/s — downward, not zero.
The student's reasoning would only be correct if the ball returned to its launch height (where vertical displacement WOULD be zero), but here it lands at a lower elevation.
Why it scores: (1) Clearly states the claim is incorrect. (2) Uses the correct definition of average velocity (displacement / time). (3) Correctly identifies that displacement is not zero because the start and end points are at different heights. (4) Optional bonus: explains WHEN the student's reasoning would be correct, showing deep understanding.
How to score points on AP Physics 1 FRQs
Show every step. Graders give partial credit, so even if your final answer is wrong, clearly written setup, equations, and substitutions earn points.
Define your coordinate system early. State "Taking up as positive" or "Taking right as positive" at the start of each problem to avoid sign confusion.
Write the equation in symbols first. Then substitute numbers. This shows you know the physics, not just arithmetic.
Always include units. An answer of "5" without units does not earn full credit. An answer of "5 m/s" does.
For explanation questions, give the WHY. "The ball decelerates" doesn't score; "the ball decelerates because gravity pulls opposite to its upward velocity" does.
Sketch a diagram. Especially for 2D problems, a clear labeled sketch helps you set up the problem AND helps graders see your thinking.
Don't repeat the question. Get straight to your work — exam time is precious.