In uniform motion an object travels at a constant speed in a straight line. The distance travelled is found using distance (m) = speed (m/s) × time (s). Rearranged, speed = distance ÷ time and time = distance ÷ speed. A runner at a constant 4 m/s for 50 s travels 4 × 50 = 200 m.
In uniform acceleration the velocity changes by the same amount every second. Acceleration (m/s2) = change in velocity (m/s) ÷ time (s). A car whose velocity goes from 0 to 12 m/s in 4 s has an acceleration of 12 ÷ 4 = 3 m/s2, which is read as metres per second squared.
When you know the acceleration and the distance but not the time, use the equation (final velocity)2 − (initial velocity)2 = 2 × acceleration × distance. In symbols this is v2 − u2 = 2as, where v is the final velocity, u is the initial velocity, a is the acceleration and s is the distance.
Worked example: a car starts from rest, so u = 0, and accelerates at 2 m/s2 over 25 m. Then v2 = 0 + 2 × 2 × 25 = 100, so v = 10 m/s. Remember to take the square root at the end.