In uniform motion an object moves at a constant speed, so distance = speed × time. With distance in metres, speed in m/s and time in seconds, a van moving at 15 m/s for 40 s travels 600 m. The equation can be rearranged: speed = distance ÷ time and time = distance ÷ speed.
In uniform acceleration the velocity changes by the same amount every second. Acceleration = change in velocity ÷ time taken, or a = (v − u) ÷ t. Here u is the initial velocity, v is the final velocity and the unit of acceleration is m/s2. A car going from rest to 12 m/s in 4 s has a = 12 ÷ 4 = 3 m/s2.
When the time is not known, use v2 − u2 = 2as, where s is the distance in metres. A car starts from rest (u = 0) and accelerates uniformly at 3 m/s2 over 24 m. Then v2 = 0 + 2 × 3 × 24 = 144, so v = 12 m/s. As a check, it takes 4 s and covers 24 m at an average of 6 m/s.
To choose the right equation, write down the quantities you are given and the one you want. Keep the units consistent, and remember that an object starting from rest has u = 0.