Distance, displacement, speed and velocity
Distance is how far an object travels along its path. Displacement is how far it is from where it started, in a straight line, with a direction. Speed is distance per unit time. Velocity is speed in a given direction.
- initial velocity (m/s)
- final velocity (m/s)
- acceleration (m/s²)
- time (s)
Equations of uniformly accelerated motion
| Equation | When to use it |
|---|---|
| v = u + at | no distance needed |
| s = ut + ½at² | no final velocity needed |
| v² = u² + 2as | no time needed |
Choose a starting velocity and an acceleration. The graphs show velocity against time (a straight line) and distance against time (a curve that bends upward when speeding up).
A car moving at 20 m/s brakes steadily and stops in 4 s. Find its acceleration and the distance it travels while stopping.
- u = 20, v = 0, t = 4.
- Distance.
Answer: The acceleration is −5 m/s² (a deceleration) and the stopping distance is 40 m.
Graphs of motion
Graphs show motion at a glance. On a distance–time graph the gradient is the speed: a flat line means the object is not moving and a steeper line means a faster object. On a velocity–time graph the gradient is the acceleration, and the area under the line is the distance travelled.
Motion under gravity
Near the Earth every freely falling object, heavy or light, has the same acceleration: m/s² (about 10 m/s²) downwards, when air resistance is ignored. Use the same equations with .
Key terms
- Displacement
- Straight-line distance from the start, with direction.
- Velocity
- Speed in a stated direction.
- Acceleration
- Rate of change of velocity.
- Free fall
- Falling under gravity alone.
Summary
- Speed = distance ÷ time; acceleration = (v − u) ÷ t.
- For constant acceleration: v = u + at, s = ut + ½at², v² = u² + 2as.
- Free fall has a = g ≈ 9.8 m/s² downwards.
- Distance–time graph: gradient = speed. Velocity–time graph: gradient = acceleration, area = distance.