Motion with Multiple Parts Video Lessons

Concept

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

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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?