You are driving to the grocery store at 20 m/s. You are 110 m from an intersection when the light turns red. You have a reaction time of 0.70 seconds before applying the brakes. a) How far from the intersection are you when you hit the brakes?
b) What deceleration is required to stop at the intersection?
c) How long does it take you to stop?

a)

reaction time = 0.70 s

distance travelled in reaction time = v*t

= 20 m/s * 0.70 s

= 14 m

So, when brake is applied, distance remaining= 110 m - 14 m = 96 m

96 m

b)

vf = 0 m/s

d = 96 m

vi = 20 m/s

use:

vf^2 = vi^2 + 2*a*d

0 = 20^2 + 2*a*96

-400 = 2*a*96

a = -2.08 m/s^2

-2.08 m/s^2

c)

use:

vf = vi + a*t

0 = 20 - 2.08*t

t = 9.6 s

9.6 s

Explanation:

the tires are rotating at 0.434 rpmlinear speed=45 m/sdiameter=0.550 mradius=0.275 mnow v= rωω= v/rω=45/0.275ω=163.6 rad/sω=163.6 rad/s (1rev/2π rad) (60s/1m)ω=1563 rpm