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Speed & Acceleration Calculator
Speed, average speed, acceleration and uniform motion — any two knowns give the third
Given distance and time, find speed; its direction matches the displacement.
Speed v6m/s
m/s6
km/h21.6
Total distance120 m
Total time20 s
4 / 4
- 1Formula
Speed is distance divided by time, in the direction of the displacement.
- 2Substitute
Substitute the known values into the formula.
- 3Solve
The result is shown in both m/s and km/h (1 m/s = 3.6 km/h).
- 4Check
Checking with s = vt reproduces the given distance.
Concept
Velocity describes how fast position changes and is a vector. Average velocity is total displacement over total time, not the mean of segment velocities.
Acceleration describes how fast velocity changes: a = (v − u)/t. Same direction as v means speeding up, opposite means slowing down.
Going further
- The four kinematic equations
- v = u + at, s = ut + ½at², v² = u² + 2as, s = (u + v)t/2. Only two are independent, so any three knowns determine the rest.
- The v-t graph
- The slope of a v-t graph is acceleration and the area under it is displacement; uniform acceleration is a straight line.
- Free fall and vertical throws
- Free fall is uniform acceleration with u = 0 and a = g. A vertical throw is the same motion with a = −g, and rise and fall take equal times.
Common mistakes
- Average speed ≠ mean speed: 100 m in 10 s then 100 m in 20 s gives 6.67 m/s, not 7.5 m/s.
- Unify units first. Convert km/h to m/s by dividing by 3.6 before substituting.
- For braking, first find the stopping time t = u/∣a∣; beyond it the displacement no longer follows the formula.