The figure below shows a graph of angular velocity as a function of time for a car driving around a circular track. Through how many radians does the car travel in the first 10 minutes?
A)30
B)50
C)70
D)90
E)100

Question

The figure below shows a graph of angular velocity as a function of time for a car driving around a circular track. Through how many radians does the car travel in the first 10 minutes? 
A)30 
B)50 
C)70 
D)90 
E)100

Quizplus · Accepted Answer

From the graph, we can see that the angular velocity is constant for the first 5 minutes and equal to 0.4 rad/min. Therefore, in the first 5 minutes, the car travels 
distance= velocity x time = (0.4 rad/min) x (5 min) = 2 radians 
For the next 5 minutes, the angular velocity increases linearly from 0.4 rad/min to 1.0 rad/min. The average angular velocity over this interval is (0.4+1.0)/2 = 0.7 rad/min. Therefore, in the next 5 minutes, the car travels 
distance = velocity x time = (0.7 rad/min) x (5 min) = 3.5 radians
The total distance traveled by the car in the first 10 minutes is 
2 radians + 3.5 radians = 5.5 radians 
Since the car is traveling around a circular track, we know that the distance traveled in radians is equal to the angle traveled in radians. Therefore, the car travels 5.5 radians in the first 10 minutes. 
The closest answer choice to 5.5 radians is 70, so the best choice is (C) 70.

The Figure Below Shows a Graph of Angular Velocity as a Function