Step-by-step explanation:
(a)
The initial kinetic energy is geven by 1/2 m v^2, all of which we are given in the problem.
KE = 1/2 (1500) (32)^2 = 768000 J
(b)
Use the work-kinetic energy theorem. The work-kinetic energy theorem states that the net work done by the forces on an object equals the change in its kinetic energy.
ΔKE = KEf - KEi
Since, the car ends at rest (no velocity), the final kinetic energy is 0.
ΔKE = -KEi = -768000 J
Apply the work kinetic energy theorem.
ΔKE = W = -768000 J
(c)
W = F · d = F d cosα
We are given d, and we have W from part b. In this case, α is 180° since the force must be in the opposite direction of the motion to slow the car down. Rearrange the equation for F.
F = W / (d cosα) = -768000 / (21 cos180°) = 36571 N
(d)
The force causing the car to stop is the frictional force, caused by the car's tires rubbing against the pavement.