Key ideas
Kinematics describes motion with position, velocity and acceleration, without asking what causes it. With constant acceleration, four equations connect displacement, time, and the initial and final velocity.
- Velocity is the rate of change of position and acceleration is the rate of change of velocity. Both are vectors, so direction (the sign) matters.
- Average speed is total distance divided by total time. Average velocity is displacement divided by time and can be zero for a round trip.
- With constant acceleration, pick the equation that leaves out the quantity you neither know nor need: final velocity, time, displacement or acceleration.
- Free fall near Earth’s surface is constant acceleration of about 9.8 m/s² downward, whatever the mass.
Key equations
v = v₀ + atx = x₀ + v₀t + ½at²v² = v₀² + 2a(x − x₀)x − x₀ = ½(v₀ + v)t
Worked example
A car brakes uniformly from 20 m/s to rest in 5.0 s. Acceleration: a = (0 − 20) ÷ 5.0 = −4.0 m/s². Stopping distance: x = ½(v₀ + v)t = ½ × 20 × 5.0 = 50 m. Check with v² = v₀² + 2ax: 0 = 400 + 2(−4.0)x gives x = 50 m.
Common mistakes
- Mixing units, such as km/h for speed with seconds for time. Convert to m/s first by dividing km/h by 3.6.
- Using the constant-acceleration equations when the acceleration changes, or forgetting that slowing down is a negative acceleration.
- Thinking the acceleration is zero at the top of a throw. The velocity is zero there, but the acceleration is still g.
Practice
Test yourself with practice questions on this topic: Kinematics