Describing motion with speed, velocity and acceleration
Distance is the total length of path travelled, while displacement is the shortest straight-line distance from start to finish with a direction. If you walk once around a circular park and return to the gate, your distance is the circumference but your displacement is zero. Speed is distance per unit time, and velocity is displacement per unit time, so velocity includes direction.
Acceleration is the rate of change of velocity, a = (v − u)/t, measured in m/s². A car slowing down has negative acceleration, also called retardation. For uniform acceleration, three equations describe motion: v = u + at, s = ut + ½at² and v² − u² = 2as. These can be derived from a velocity–time graph, whose slope is acceleration and whose area gives displacement. For instance, a car starting from rest with an acceleration of 2 m/s² reaches 20 m/s in 10 s and covers 100 m. Uniform circular motion has constant speed but changing velocity.
Why it matters
These ideas explain stopping distances on roads, why speed limits differ near schools, and how GPS apps estimate arrival time. Athletes and coaches analyse acceleration to improve performance. The equations of motion are the starting point for Newton’s laws, gravitation and almost every mechanics problem in later classes.
Key terms
- Displacement
- The shortest distance between the initial and final positions of an object, with direction.
- Velocity
- The rate of change of displacement, including both speed and direction.
- Acceleration
- The rate at which an object’s velocity changes with time.
- Uniform circular motion
- Motion along a circle at constant speed, with direction changing continuously.