AP Physics 1 kinematics, made clear

By Ashraf Bhura, Co-Founder, STEM-Tutor · Updated October 2026

Kinematics is Unit 1 of AP Physics 1 and the base for everything after it. Here are the ideas, equations and graph skills you need.

The core quantities

• Displacement: change in position, with a direction.
• Velocity: rate of change of position.
• Acceleration: rate of change of velocity.

All three are vectors. A negative sign means a direction, not "less".

The constant-acceleration equations

• v = v₀ + at
• x = x₀ + v₀t + ½at²
• v² = v₀² + 2a(x − x₀)

Write down what you know and what you want, then pick the equation that uses only those quantities. They only work when acceleration is constant.

Motion graphs

• The slope of a position-time graph is velocity.
• The slope of a velocity-time graph is acceleration.
• The area under a velocity-time graph is displacement.
• The area under an acceleration-time graph is the change in velocity.

Many exam questions give a graph and ask you to describe the motion in words, or draw a matching graph. Practise both directions.

Projectiles

Treat the horizontal and vertical motion separately. Horizontally, velocity is constant if air resistance is ignored. Vertically, acceleration is g downward. The time is the same for both, and that is usually how you link them.

Common mistakes

• Thinking an object at the top of its flight has zero acceleration. Its velocity is zero; its acceleration is still g.
• Mixing up distance and displacement.
• Using the equations when acceleration changes.
• Forgetting to choose a positive direction and stick to it.

How to practise

1. Start each problem by sketching the motion and listing known quantities.
2. Convert every word problem into a velocity-time graph at least once.
3. Do mixed problems, so you practise choosing the method, not just using it.

Worked examples

Example 1: reading a velocity-time graph

A cart's velocity rises steadily from 2 m/s to 8 m/s in 3 s.

• Acceleration = gradient = (8 − 2)/3 = 2 m/s².
• Displacement = area = ½(2 + 8) × 3 = 15 m.

Example 2: choosing the equation

A ball rolls up a slope at 6 m/s and slows at 1.5 m/s². How far up does it go?

• v = 0 at the top, v₀ = 6, a = −1.5. Time is not needed.
• v² = v₀² + 2aΔx: 0 = 36 − 3Δx, so Δx = 12 m.

Example 3: a projectile launched at an angle

A ball is launched at 20 m/s at 30° above the horizontal from level ground. Find its time of flight and range. Use g = 9.8 m/s².

• Components: v_x = 20 cos30° ≈ 17.3 m/s and v_y = 20 sin30° = 10 m/s.
• Time to the top: 10/9.8 ≈ 1.02 s, so time of flight ≈ 2.04 s on level ground.
• Range = 17.3 × 2.04 ≈ 35.3 m.

Example 4: relative motion

A boat moves at 4 m/s relative to the water, straight across a river flowing at 3 m/s. What is its speed relative to the bank?

• The velocities are perpendicular, so speed = √(4² + 3²) = 5 m/s.

Practice questions

Try each one before opening the answer.

Frequently asked questions

Do I need to memorise the kinematics equations?

No, they are on the equation sheet. Practise choosing between them and checking that acceleration is constant.

Is air resistance included?

Usually not, unless the question says so. If it is, the acceleration is no longer constant and the equations do not apply.

The key ideas in more depth

Speed versus velocity

Speed tells you how fast; velocity tells you how fast and in which direction. A car going round a roundabout at a steady 20 km/h has constant speed but changing velocity. That difference matters later for circular motion.

Acceleration does not mean speeding up

Acceleration is any change in velocity. If velocity and acceleration point the same way, the object speeds up. If they point opposite ways, it slows down. Many AP questions test this with graphs where velocity is positive but acceleration is negative.

Graphs are the heart of the unit

Expect to convert between position-time, velocity-time and acceleration-time graphs. A useful rule: the slope of one graph gives the next graph down, and the area under one graph gives the change in the graph above.

Exam tips

• Label axes and units on every graph you draw.
• For projectiles, make a table with separate horizontal and vertical columns.
• State "acceleration is constant" before using the kinematics equations in free-response answers.

More practice

Try each one before opening the answer.

More questions students ask

What is the difference between distance and displacement?

Distance is the total path length; displacement is the straight-line change in position, with a direction. A lap of a track has a large distance but zero displacement.

Why do heavier objects not fall faster?

A heavier object feels a bigger gravitational force, but it also has more inertia, so the acceleration is the same: g.

How do I know which kinematics equation to use?

List the quantities you know and want. Choose the equation that contains only those.

Extra practice

Try each one before opening the answer.

Key takeaways

• Displacement, velocity and acceleration are vectors.
• The kinematics equations need constant acceleration.
• Slope and area link position, velocity and acceleration graphs.
• Treat projectile motion as separate horizontal and vertical motions.
• At the top of a projectile's path, acceleration is still g.

Quick check