You're driving down the highway late one night at 18m/s when a deer steps onto the road 39m in front of you. Your reaction time before stepping on the brakes is 0.50s , and the maximum deceleration of your car is 12m/s2 .
How much distance is between you and the deer
when you come to a stop?
What is the maximum speed you could have and still not hit the deer?
a) Mind you before your reaction time, you had be going at a uniform speed 18m/s, so for the reaction time of 0.5 seconds, you had covered a distance of:
18m/s*0.5s = 9 m
For the second part which involved deceleration, using:
v = u - at, Noting that there is deceleration.
u = 18m/s, v = final velocity = 0, a = -12m/s².
Let us solve for the time.
v = u + at
0 = 18 - 12*t
12t = 18
t = 18/12 = 1.5 seconds.
Let us compute for the distance covered during the 1.5s
s = ut + 1/2at², a = -12 m/s²
s = 18*1.5 -0.5*12*1.5² = 13.5m
So the total distance covered = Distance covered from reaction time + Distance covered from deceleration
= 9m + 13.5m = 22.5m
So you have covered 22.5m out of the initial 39m.
Distance between you and the dear: 39 - 22.5 = 6.5m
So you have 6.5m between you and the deer. So you did not hit the deer.
b) Maximum speed you still have:
Well through trial and error, if you maintain the same values of deceleration, reaction time, distance between the car and the deer, you could have a speed of 25 m/s and still not hit the deer. Once it is higher than that by a significant amount you would hit the deer.