Summary
A body moves when its position changes relative to a frame of reference, so motion is relative: you are at rest relative to the train and moving relative to the track. The path is the line it traces; the distance travelled adds up the whole route, and the displacement only looks at where it started and where it ends. Average speed is distance over time, and acceleration is how much the velocity changes each second (m/s²).
In uniform linear motion the velocity does not change: x = x₀ + v · t. In uniformly accelerated motion the velocity always changes by the same amount: v = v₀ + a · t and x = x₀ + v₀ · t + ½ · a · t². Free fall is uniformly accelerated motion with a = g ≈ 9.8 m/s², the same for every body if there is no air. On graphs, the slope of the x-t graph is the velocity and the slope of the v-t graph is the acceleration; the area under the v-t graph is the distance travelled.
Key points
- Motion is relative: it depends on the frame of reference.
- Distance travelled ≠ displacement if the object comes back.
- Average speed = distance ÷ time; from km/h to m/s divide by 3.6.
- Uniform motion: constant velocity, x = x₀ + v · t.
- Uniform acceleration: v = v₀ + a · t and x = x₀ + v₀ · t + ½ · a · t².
- Free fall: a = g ≈ 9.8 m/s², the same for all without air.
- Slope of x-t = velocity; slope of v-t = acceleration.
- Area under v-t = distance travelled.