Question

You are driving to the grocery store at 18 m/sm/s. You are 160 mm from an intersection when the traffic light turns red. Assume that your reaction time is 0.50 ss 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?

Answer 1

part(a) 151 m

part(b) 1.073 m/s2

part(c) 16.7 secs

Explanation:Firstly the person applied brakes 0.5 secs after seeing the red light hence the distance traveled during this time is

d=v*t

d=18*0.5

d=9m

For part (a)

I have corrected this question and now

The person was 160m from the intersection before applying the brakes as he traveled 9m before the brakes

He is now 151 m from intersection as

s=160-9

s= 151 m

part (b)

As it is given that velocity of the car is 0 at the intersection so we use this information in kinematic equation

`v^2=u^2+2as`

here u=18m/s and s=151

`0=18^2+2a*151\\302a=-324\\a=-1.073 m/s^2`

To calculate time we can use the acceleration equation

`a=(v-u)/(t) \\t=(v-u)/(a)\\t=18/1.073\\t=16.77 secs`