Question

You are driving at night on a highway at a speed of 18.2m/s. All of a sudden you see a deer in the road 38.3 m ahead.
a. If you can slow down at a maximum rate of 4.50 m/s², what reaction time is required to avoid hitting the deer?
b. If your reaction time is actually 0.300s, how fast will you be traveling when you hit the deer?

Answer 1

Start by finding how long it will take for the car to slow to a stop. Use the equation (Vf)^2 = (Vi)^2 + 2ad with Vf = 0 and Vi = 18.2. Solve for d.

d = 36.8044 (this is the minimum distance required to stop if the reaction time was 0s)

Find the difference between d and 38.3 which equals 1.495556m

Now divide this distance by the speed to get a reaction time that won't hit the deer

a) Reaction time = 0.08217

For part b, multiply the reaction time by the speed to get how far the car travels before the driver sees the deer.

This distance is (0.3)*(18.2) = 5.46m

Then using the same kinematic equation as before plug in the distance to the deer (38.3 - 5.46 = 32.84) for d and solve for Vf.

(Vf)^2 = (18.2)^2 + 2*(-4.5)*(32.84)

b) The car will hit the deer at 5.97327m/s