Asked by Bre
You are driving at 20 m/s when you notice a tree blocking the road, 30 meters ahead of you. It takes you half a second to react before slamming on the brakes. Your car decelerates at a constant 10 m/s2. How far does your car travel before stopping? Will you hit the tree?
Answers
Answered by
Reiny
everything happens starting at t=.5
a = -10
v = -10t + c
when t = .5 , v = 20
20 = -10(.5) + c
c = 25
v = -10t + 25 , for t ≥ .5
s = -5t^2 + 25t + k
when t = .5 , the car goes goes another 20(.5) or 10 m
so when t = .5, the remaining distance is 20 m
20 = -5(.5)^2 + 25(.5) + k
k = 8.75
s = -5t^2 + 25t + 8.75
the car stops when v = 0
0 = -10t + 25
t = 2.5
when t = 2.5
s = -5(2.5)^2 + 25(2.5) + 8.75
= 40
Unfortunately the tree was in the way, and yes, you are going to hit it
a = -10
v = -10t + c
when t = .5 , v = 20
20 = -10(.5) + c
c = 25
v = -10t + 25 , for t ≥ .5
s = -5t^2 + 25t + k
when t = .5 , the car goes goes another 20(.5) or 10 m
so when t = .5, the remaining distance is 20 m
20 = -5(.5)^2 + 25(.5) + k
k = 8.75
s = -5t^2 + 25t + 8.75
the car stops when v = 0
0 = -10t + 25
t = 2.5
when t = 2.5
s = -5(2.5)^2 + 25(2.5) + 8.75
= 40
Unfortunately the tree was in the way, and yes, you are going to hit it
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