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?

1 m

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

2 m/s2

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

(a) 95m

(b) - 2.11m/s^2

(c) 9.5s

Explanation:

(a). out of remaining 105m, for initial 0.5s I travel with constant speed:

distace covered = 0.5s * 20m/s = 10m

it means that I am 105-10 = 95m away from the intersection

(b) we apply the second equation of motion

v^2 - u^2 = 2*a*s

so s = 95 m

u = initial velocity = 20 m/s

v = final velocity = 0 m/s (comes to rest)

0^2 - 20^2 = 2*a*95

solving for 'a'

a = - 2.11 m/s^2

(c)

v-u = at

0 - 20 = - 2.11*t

solving for time t

t = 9.5s