A 2000 kg car moves down a level highway under the actions of two forces. one is a 1060 n forward force exerted on the drive wheels by the road; the other is a 1010 n resistive force. use the work-energy theorem to find the speed of the car after it has moved a distance of 21 m, assuming it starts from rest.

Question

Physics

Duncan Haynes

28 November, 08:14

A 2000 kg car moves down a level highway under the actions of two forces. one is a 1060 n forward force exerted on the drive wheels by the road; the other is a 1010 n resistive force. use the work-energy theorem to find the speed of the car after it has moved a distance of 21 m, assuming it starts from rest.

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Vicente Pacheco · Answer 1

Refer to the diagram shown below.

The net force acting on the vehicle is

F - R = 1060 - 1010 = 50 N

The distance traveled is 21 m. Because the force is constant, the work done is

W = (50 N) * (21 m) = 1050 J

Assume that energy is not dissipated by air resistance or otherwise.

Conservation of energy requires that W = KE, where KE is the kinetic energy of the vehicle.

The KE is

KE = (1/2) * (2000 kg) * (v m/s) ² = 1000v² J

Equate KE and W to obtain

1000v² = 1050

v² = 1.05

v = 1.025 m/s

Answer: 1.025 m/s