Displacement while accelerating
When an object's velocity increases or decreases by the same amount every second, it is said to have a uniform acceleration or a uniform deceleration.
For such an object you cannot use "displacement = velocity × time" directly, because the velocity is not one value. So which velocity should be used?
The answer: the average velocity
Since the object moves with a uniform acceleration, the average velocity can be found by adding the initial and final velocities and dividing by two.
displacement = average velocity × time
Example
An object starting from rest undergoes a uniform acceleration for 6 seconds and reaches a velocity of 12 m s−1. What is its displacement in that time?
Solution
initial velocity = 0 (that is what "from rest" means)
final velocity = 12 m s−1
average velocity = (0 + 12) ÷ 2 = 6 m s−1
displacement = 6 m s−1 × 6 s = 36 m
Three formulae — which one, when?
Velocity constant: displacement = velocity × time
Acceleration uniform: displacement = average velocity × time
Looking for acceleration: acceleration = change in velocity ÷ time
The first two are really the same thing — at a constant velocity, the average velocity is that velocity.