You're driving down the highway late one night at 20 m/s when a deer steps onto the road 57 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.
A. How much distance is between you and the deer when you come to a stop?
B. What is the maximum speed you could have and still not hit the deer?

Explanation:

Lets calculate the distance that the car has traveled first.

a)

as the car was traveling with the constant speed.

×

d = (20)(0.5) = 10 m    (1)

now we will calculate the distance that is required in order to stop the car.

0 = (20)²+ 2(-10)

= 20 m       (2)

now by using (1) and (2) we can find out the total distance traveled y the car before it stops.

Distance between the car and the deer when it stops = 57 - 30 = 27 m

b)

lets calculate the maximum speed you could have and still not hit the deer.

we have

total distance traveled before stopping = 57 m

we must calculate the distance for reaction time with constant speed.

0 = + 2(-10)(57- 0.5)

Apply the quadratic equation on it.

= -b±

       a = 1

       b = 10

       c = -1140

by putting these values we got

we neglect the negative value.

m/s