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.

Answer:
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.
$$\begin{array}{l}\text{Average Speed = }\frac{\text{Toral Distance Travelled}}{\text{Total Time Taken}}\\ \text{Average Speed = }\frac{30}{6}=5.0m{s}^{-1}\end{array}$$

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

Reference

$$\begin{array}{l}v=u+at\\ s=ut+\frac{1}{2}a{t}^2\\ v^2=u^2+2as\\ s=\frac{1}{2}(u+v)t\end{array}$$