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Question

A 2000 kg car accelerates from rest under the actions of two forces. One is a forward force of 1140N provided by traction between the wheels and the road. The other is a 950N resistive force due to various frictional forces. Use the work-kinetic energy theorem to determine how far the car must travel for it's speed to reach 2.0m/s.

Answer 1

The work done on the car by the net force equals the change on the car's kinetic energy.

Work = Force * distance
KE = 1/2 mv^2

We are given a mass for the car and the final velocity, so from this we can calculate the car's final KE,
KE = 1/2 (2000 kg) * (2 m/s)^2
KE = 4000 Joules

Since in this case, KE = W
W = 4000 Joules = F * d

We know the net force to be the sum of all the forces acting on th car. Since there is a "forward" force of 1140 Newtons and a "backward" (what we will call 'negative') force acting on the car of 950 N, the net force is 1140 - 950 = 190 Newtons

W = 4000 J = (190 N) * d
d = 4000 J / 190 N
d = 21.05 meters

Answer 2

Change in energy = work

Work = force x distance

Energy = 1/2(mv^2)

Starting at rest the initial energy is zero. The net force applied to the car is 1140 N - 950 N = 190 N.

The change in energy (work) is equal to the final energy since the initial was zero. W = 1/2(2000 kg)(2 m/s)^2 = 4000 Joules

W = Fd, so d = W / F

d = 4000 J / 190 N = 21.05 meters

Answer 3

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Answer 4

ke=1/2m*v^2=1/2*2000*2^2=4000J
W=F*D
need Fnet=1140-950=190N
D=W/F
W=kinetic energy in this case, so
D=4000/190=21.1m