Mastering physics?

Question

You're driving down the highway late one night at 18 m/s when a deer steps onto the road 40m in front of you. Your reaction time before stepping on the brakes is 0.50s, and the maximum deceleration of your car is 10 m/s^2

How much distance is between you and the deer when you come to a stop?

and

What is the maximum speed you could have and still not hit the deer?

Answer 1

For t1=0.50s you move with constant velocity so:

x1=v*t1=18m/s*0.50s=9m

Then

vf=vi-a*t2-->0=18-10*t2-->

t2=1.8s

so

x2=vi*t2-.5*a*t2^2

x2=18*1.8-0.5*10*1.8^2=16.2m

So distance is between you and the deer: 40m-16.2m=23.8m

b) You must stop at 40m so:

40=18*t3-0.5*10*t3^2

solve for t 3

vf=vi-a*t2--> vi=a*t3