# Motion with Uniform Acceleration - Example 7

Example 7
A body is accelerated uniformly from rest and in the first 6.0 s of its motion it travels 30 m. Find
1. the average speed for this period of 6 s,
2. the speed at the end of this period,
3. the acceleration.
It's advisable to list down all the information that we have.

Initial velocity, u = 0 (Because the motion start from rest)
Time taken, t = 6.0s
Displacement, s = 30m
Final velocity, v = ?
Acceleration, a = ?

i.

ii. The acceleration, a, is not involved, hence we select the equation $$s = \frac{1}{2}(u + v)t$$to solve the problem. $(30)= 1 2 [(0)+v](6) 3v=30 v=10m s −1$
ii. The final velocity, v, is not involved, hence we select the equation $$s = ut + \frac{1}{2}a{t^2}$$ to solve the problem. $s=ut+ 1 2 a t 2 (30)=(0)(6)+ 1 2 a ( 6 ) 2 18a=30 a= 5 3 m s −2$

### Reference

$v=u+at s=ut+ 1 2 a t 2 v 2 = u 2 +2as s= 1 2 (u+v)t$