Motion with Uniform Acceleration - Example 6

Example 6
A car begins to move from rest. The velocity of the car increases at a rate of 4 ms^-2. Find the distance traveled by the car after 12 second.

Answer:
It's advisable to list down all the information that we have.

Initial velocity, u = 0 (Because the begins to move from rest)
Acceleration, a = 4 ms^-2 (Rate of increment = Acceleration)
Time taken, t = 12s
Displacement, s = ?

The final velocity, v, is not involved, hence we select the equation \(s = ut + \frac{1}{2}a{t^2}\) to solve the problem. $$\begin{array}{l}s=ut+\frac{1}{2}a{t}^2\\ s=(0)(12)+\frac{1}{2}(4){(}^{12}\\ s=288m\end{array}$$

Reference

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