Question

You are driving to the grocery store at 20 m/s. You are 110 m

from an intersection when the traffic light turns red. Assume

that your reaction time is 0.50 s and that your car brakes with

constant acceleration. What magnitude braking acceleration will bring you to a stop exactly at the intersection?

Short answer

The magnitude of breaking acceleration to bring the car at a rest is$2m/s^2.$

Step-by-step solution

Given information

Initial velocity $u=20m/s$, Reaction time $t=0.5s$, Distance of intersection,$d=110m.$

Calculation

The distance travelled after pressing the brake is, $$\begin{gathered} s=ut \\ s=\left(20\times 0.5\right)m \\ s=10m \end{gathered}$$

So the distance traversed before pressing the brake is, $D=\left(110-10\right)m=100m.$

Find the magnitude of acceleration

We can find the acceleration by using the formula,

$v^2=u^2+2Da$, where $v\to finalvelocity,a\to acceleration$.

The final velocity of the car should be, $v=0$at the time of stopping.

Therefore, the acceleration to bring the car at a stop can be determined as,

$$\begin{gathered} 0=u^2+\left(2a\times 100\right) \\ a=-\frac{u^2}{200} \\ a=-\frac{{20}^2}{200} \\ a=-2m/s^2 \end{gathered}$$

Therefore the magnitude of acceleration to bring the car at a rest is $2m/s^2.$