Problema Solution
the driver of a car slams on the brakes when he sees a tree blocking the road. the car slows uniformly with an acceleration of -5m/s2 for 4.20s, making straight skid marks 62.4m long, all the way to the tree. With what speed does the car then strike the tree?
Answer provided by our tutors
a = -5.60 m/s^2
t = 4.20 s
x(t) - x0 = 62.4 m
v = final velocity
v0 = initial velocity
v(t) = v0 + at
x(t) = (1/2)at^2 + v0t + x0
v0 = (1/t)(x - x0) - (1/2)at plug into v(t) = v0 + at
v(t) = (1/t)(x - x0) - (1/2)at + at
v(t) = (1/t)(x - x0) + (1/2)at
v(t) = (1/4.20)*62.4 + (1/2)*(-5)*4.20
v(t) = 4.357 m/s
Therefore the car hits the tree at a speed of approximately 4.357 m/s.