You are driving down the highway late one night at 20 m/s when a deer steps onto the road 35 m in front of you. Your reaction time before stepping on the brakes is 0.50 s, and the maximum deceleration of your car is 10 m/s2. How much distance is between you and the deer when you come to a stop?

So the dear is 35m away from the car that is running at a speed of 20m/s where your reaction time in hitting the brakes is 0.5s and the cars deceleration is 10 m/s2. By calculating i came up with an answer of 5meters, the car only have 5 meters away from the deer to hit it.

A) Mind you before your reaction time, you had be going at a uniform speed 20m/s so for the reaction time of 0.5 seconds, you had covered a distance of:

20m/s*0.5s = 10 m

For the second part which involved deceleration, using:

v = u - at, Noting that there is deceleration.

u = 20m/s, v = final velocity = 0, a = - 10m/s².

Let us solve for the time.

v = u + at

0 = 20 - 10*t

10t = 20

t = 20/10 = 2 seconds.

Let us compute for the distance covered during the 2s

s = ut + 1/2at², a = - 10 m/s²

s = 20*2 - 0.5*10*2² = 20m

So the total distance covered = Distance covered from reaction time + Distance covered from deceleration

= 10m + 20m = 30m

So you have covered 30m out of the initial 35m.

Distance between you and the dear: 35 - 30 = 5m

So you have 5m between you and the deer. So you did not hit the deer.