Question

A car is travelling at 20 m/s along a road. A child runs out into the road 50 m ahead and the car driver steps on the brake pedal. What must the car's deceleration be if the car is to stop just before it reaches the child?

Answer 1

We have to find the deceleration. We have the following information given,
Initial velocity, (u) = 20 m/s
Final velocity, (v) = 0 m/s
Distance travelled, (s) = 50 m
Let the deceleration for the entire journey be (a)
We can calculate acceleration by using the 3^rd equation of motion,
$a=\frac{v^2-u^2}{2s}$
Where,
(s) - Displacement
(u) - Initial velocity
(a) - Acceleration
(v) - Final velocity
Put the values in above equation to find the deceleration,
$$\begin{gathered} a=\left[\frac{0-400}{2\left(50\right)}\right]\mathrm{m}/{\mathrm{s}}^2 \\ =\left(-\frac{400}{100}\right)\mathrm{m}/{\mathrm{s}}^2 \\ =\boxed{-4\mathrm{m}/{\mathrm{s}}^2} \end{gathered}$$
Hence, deceleration is 4 m/s².