Can someone help me with this question?

Question

You are driving to the grocery story at 20 m/s. You are 110 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 after the light changes?

Am I supposed to use equations and plug the numbers at the beginning of the question into whichever equations they may be? There are three different kinematic equations for motion with constant acceleration. Would I use one of them. I am not quite sure which to use if I am to use them.

Answer 1

Start with motion at constant speed: You see the light turn red and 0.5 s later you hit the brake. SO in the 0.5 sec you travel

d = v*t = 20 m/s*0.5s = 10 m That's part a.

Now you have only 110 -10 = 100 m in which to stop. You are moving at 20 m/s when you begin to brake and you want to come to rest at the intersection. So you can use:

x =(v^2 - v0^2)/(2a) to solve for a ---> a =(v^2 - v0^2)/(2x)

a = (0^2 - 20^2)/(2*100) = -400 m^2/s^2/200m = -2 m/s^2

The "-" sign indicates you are deccelerating.

Since you know a, you can use:

v = at+v0 and solve for t t=(v-v0)/a = (0 - 20)/(-2) = 10 sec