A motor develops power as shown in the graph. The energy expended by the motor in the time interval between t = 10 s and t = 30 s is
A) 1.0 J
B) 1.3 J
C) 0.20 kJ
D) 0.60 kJ
E) 0.70 kJ

Question

A motor develops power as shown in the graph. The energy expended by the motor in the time interval between t = 10 s and t = 30 s is
A) 1.0 J 
B) 1.3 J 
C) 0.20 kJ 
D) 0.60 kJ 
E) 0.70 kJ

Quizplus · Accepted Answer

The energy expended by the motor is equal to the area under the power curve. We can approximate this area as a trapezoid with base lengths of 20 s (from 10 s to 30 s) and height of the average power between t=10 s and t=30 s.

The average power between t=10 s and t=30 s is:

average power = (100 W + 200 W)/2 = 150 W

Thus, the area of the trapezoid is:

Area = (1/2) x (20 s) x (100 W + 200 W) = 3000 J

Converting to kJ:

Area = 3.0 kJ

Therefore, the energy expended by the motor in the time interval between t=10 s and t=30 s is approximately 0.60 kJ (to two significant figures).

Thus, the best answer choice is D.

A Motor Develops Power as Shown in the Graph