Answer:
9.43 m/s
Explanation:
First of all, we calculate the final kinetic energy of the car.
According to the work-energy theorem, the work done on the car is equal to its change in kinetic energy:
[tex]W=K_f - K_i[/tex]
where
W = -36.733 J is the work done on the car (negative because the car is slowing down, so the work is done in the direction opposite to the motion of the car)
[tex]K_f[/tex] is the final kinetic energy
[tex]K_i = 66,120 J[/tex] is the initial kinetic energy
Solving,
[tex]K_f = K_i + W = 66,120 + (-36,733)=29,387 J[/tex]
Now we can find the final speed of the car by using the formula for kinetic energy
[tex]K_f = \frac{1}{2}mv^2[/tex]
where
m = 661 kg is the mass of the car
v is its final speed
Solving for v, we find
[tex]v=\sqrt{\frac{2K_f}{m}}=\sqrt{\frac{2(29,387)}{661}}=9.43 m/s[/tex]
