Use the figure for the question. The graph shows the speed of a light truck of mass 4000 kg coasting on neutral down a level straight road.The truck is slowing down due to air resistance and rolling friction.
-Suppose the driver decides to put the truck in gear and steps on the accelerator at 5s.What is the power needed to maintain the speed at 5s?
A)20 kW
B)40 kW
C)60 kW
D)80 kW
E)100 kW

Question

Use the figure for the question. The graph shows the speed of a light truck of mass 4000 kg coasting on neutral down a level straight road.The truck is slowing down due to air resistance and rolling friction. 
-Suppose the driver decides to put the truck in gear and steps on the accelerator at 5s.What is the power needed to maintain the speed at 5s?
A)20 kW 
B)40 kW 
C)60 kW 
D)80 kW 
E)100 kW

Quizplus · Accepted Answer

From the graph, at 5s, the speed of the truck is approximately 18 m/s. To maintain this speed, the net force on the truck should be zero. Therefore, the force due to air resistance and rolling friction must be balanced by the force due to the engine.

Using Newton's second law, F = ma, where a is the acceleration of the truck, which is zero since the truck is maintaining a constant speed. Thus, F = 0.

The force due to air resistance and rolling friction can be estimated from the graph to be approximately 8000 N. Therefore, the engine must produce a force of 8000 N.

Power is the rate at which work is done, P = Fv, where v is the velocity of the truck. At 5s, the velocity of the truck is 18 m/s. Therefore, the power needed to maintain the speed at 5s is P = (8000 N) (18 m/s) = 144000 W = 144 kW. However, this is only the instantaneous power at 5s. If we assume that the driver maintains this speed for a prolonged period, the average power would be less since the engine would not need to constantly accelerate the truck.

Among the answer choices, the closest power value is 60 kW, which is choice C.

Use the Figure for the Question