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 acceleration which brings the person to stop exactly at intersection is$2m/s^2.$

Step-by-step solution

Given data

The speed of the person while moving towards grocery shop, $v=20m/s.$

The reaction time of the person is, $t=0.5s$

The distance of intersection from the starting position of the car is, $D=110m$

Consider the person applied the brake which is at $d$distance from the starting position

Determination of the distance d

According to the question, the distance travelled by the person at a constant speed $v=20m/s$is,

$$\begin{gathered} x=vt \\ x=\left(20\times 0.5\right)m \\ x=10m \end{gathered}$$

So the person strike the brake at a distance of,

$$\begin{gathered} d=D-x \\ d=\left(110-10\right)m \\ d=100m \end{gathered}$$

Determination of acceleration

The acceleration at the point of intersection can be determined by the equation as$v_0^2=v^2+2ad$.

Therefore,

role="math" localid="1648566235908" $$\begin{gathered} v_0^2=v^2+2ad \\ 0={20}^2+\left(2a\times 100\right) \\ a=\frac{0-{20}^2}{200} \\ a=-2m/s^2 \end{gathered}$$