AP Physics 1 · Unit 1 · Topic 3 of 8 · 5 min lesson

Acceleration & Free Fall

A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 4 practice questions.

Quiz this topic · 4 questions Watch the review video ↗

The big idea

Acceleration tells you how quickly velocity changes. In free fall, gravity is the only thing acting, so the acceleration is 10 m/s² downward the whole time: on the way up, at the very top, and on the way down.

1. What acceleration means

Acceleration is the change in velocity divided by the time it took:

a = Δv / Δt

So “10 m/s² downward” means: every second, the velocity changes by 10 m/s downward. Drop a ball from rest and it is moving 10 m/s after 1 s, 20 m/s after 2 s, 30 m/s after 3 s.

Speeding up or slowing down? Compare the directions of v and a:

Same directionSpeeding up

Opposite directionsSlowing down

2. A ball thrown straight up

velocity (changes)acceleration (always 10 m/s² down)

On the way up the ball loses 10 m/s of upward speed each second. At the top it stops for an instant, but gravity is still pulling, so the acceleration is still 10 m/s² down. On the way down it gains 10 m/s each second.

Symmetry: if it lands at the height it was thrown from, the time up equals the time down, and it lands with the same speed it was thrown with.

3. Key equations and graphs

Choose up as positive, then a = −10 m/s². Pick the equation that leaves out the quantity you don’t know and don’t need.

v = v₀ + atno Δy

Δy = v₀t + ½at²no v

v² = v₀² + 2aΔyno t

The v–t graph is a straight line because the slope (the acceleration) never changes. The a–t graph is flat at −10 m/s².

4. Example, then try it

Example

A ball is dropped from rest. How fast is it moving after 3 s, and how far has it fallen?

Up = +, so v₀ = 0 and a = −10 m/s².

v = v₀ + at = 0 + (−10)(3) = −30 m/s → 30 m/s downward

Δy = v₀t + ½at² = ½(−10)(3)² = −45 m → fell 45 m

Try it · work it on paper first

A ball is thrown straight up at 20 m/s. How long until it reaches the top, and how high does it go?

List what you know (up = +): v₀ = +20 m/s, v = 0 at the top, a = −10 m/s².

Time: v = v₀ + at → 0 = 20 − 10t → t = 2.0 s

Height: v² = v₀² + 2aΔy → 0 = 400 − 20Δy → Δy = 20 m

Check with symmetry: 2 s up + 2 s down = 4 s total, matching the graph above.

Answer: 2.0 s to the top, 20 m high.

5. Common mistakes

“The acceleration is zero at the top.”Only the velocity is zero. If a were zero, the ball would stay up there.

“Heavier objects fall faster.”Without air resistance, every object has the same acceleration, g.

Mixing up signs.If up is positive, a = −10 m/s². Writing +10 here makes the ball speed up forever.

Check yourself

A ball is thrown straight up. At its highest point, what is its acceleration?

At the top v = 0, but gravity still changes the velocity by 10 m/s every second, so a = 10 m/s² downward.

Ready to practice?

4 questions on Acceleration & Free Fall, each with a hint and an explanation for every wrong answer.

Quiz this topic All of Unit 1