Consider an object moving with uniform acceleration, a. Let u be its initial velocity (at time t = 0), v, its velocity after time t and s, its displacement during this time interval. Let us see how these quantities are related to each other.

7.3.1 Relation between, v, u, a and t

According to the definition of acceleration, we have

Acceleration = Change in velocity / Time interval

or a = v - u / t

or v = u + at

With the help of this equation, we can find velocity of a uniformly accelerated object after a given time interval. Or, given any three of these quantities, fourth can be found using this equation.

Example 7.2: A car has an initial velocity of 25 ms^-1. The brakes are applied and the car stops in 2.0 s. What is the acceleration of the car?

Solution: Using (10.5), v = 0, u = 25 ms-1, t = 2.0 s
O = 25 ms^-1 + a (2.0s) hence, a = - 12.5 ms^-2
It is negative. Negative acceleration is also called deceleration.

7.3.2 Relation between s, u, a and t

From equation (10.3), we have
Displacement = (average velocity) * ( time interval )

or, s = (v + u / 2 ) t
But, v = u + at

Therefore, s = 1/2 ( u + u + at ) t = ut + 1/2 at²

s = ut +1/2 at²

If an object starts from rest, u = 0 and equation (10.6) reduces to

S= 1/2 at²

Thus, we see that the displacement of an object undergoing a constant acceleration is proportional to t², while the displacement of an object with a constant velocity (zero acceleration) is proportional to t (Equation 10.3).
A body in free fall, falls with a uniform acceleration, called acceleration due to gravity (denoted by g) and having an average value 9.8 ms^-2 near the surface of earth. For this motion the equations of motion become

v = u +gt

s = ut + 1/2 gt²

Use these concepts to do the following activity: