# Problem: You are driving to the grocery store at 20 m/s. You are 105 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.(a) How far are you from the intersection when you begin to apply the brakes?(b) What acceleration will bring you to rest right at the intersection?(c) How long does it take you to stop?

###### FREE Expert Solution

In this problem, we need to know some equations before we start the solution.

The velocity of an object is expressed as:

$\overline{){\mathbf{v}}{\mathbf{=}}\frac{\mathbf{d}}{\mathbf{t}}}$, where d is distance and t is the time taken.

We'll also need the kinematic equations:

$\overline{){{{\mathbf{v}}}_{{\mathbf{f}}}}^{{\mathbf{2}}}{\mathbf{=}}{{{\mathbf{v}}}_{{\mathbf{0}}}}^{{\mathbf{2}}}{\mathbf{+}}{\mathbf{2}}{\mathbf{a}}{\mathbf{∆}}{\mathbf{x}}}$ and

$\overline{){{\mathbf{v}}}_{{\mathbf{f}}}{\mathbf{=}}{{\mathbf{v}}}_{{\mathbf{0}}}{\mathbf{+}}{\mathbf{a}}{\mathbf{t}}}$

(a)

From the firs boxed equation, we can solve for d as:

v = d/t

d = vt

100% (464 ratings) ###### Problem Details

You are driving to the grocery store at 20 m/s. You are 105 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.

(a) How far are you from the intersection when you begin to apply the brakes?

(b) What acceleration will bring you to rest right at the intersection?

(c) How long does it take you to stop?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Motion with Multiple Parts concept. You can view video lessons to learn Motion with Multiple Parts. Or if you need more Motion with Multiple Parts practice, you can also practice Motion with Multiple Parts practice problems.