The graph shows the velocity of a particle as a function of time. In the 12 s shown, the particle travels
A) 0 m.
B) 1200 m.
C) 640 m.
D) 440 m.
E) 200 m.

Question

The graph shows the velocity of a particle as a function of time. In the 12 s shown, the particle travels
A) 0 m. 
B) 1200 m. 
C) 640 m. 
D) 440 m. 
E) 200 m.

Quizplus · Accepted Answer

The distance traveled by the particle can be found by taking the area under the velocity-time graph. From 0 to 4 seconds, the particle is moving at a constant velocity of 80 m/s, so it travels a distance of (80 m/s)(4 s) = 320 m. From 4 to 8 seconds, the velocity is decreasing at a constant rate, so the distance traveled can be found by finding the area of a trapezoid with height 80 m/s, bases of 4 s and 8 s, and height of 20 m/s, which is (1/2)(80 m/s + 20 m/s)(4 s) = 240 m. From 8 to 12 seconds, the particle is moving at a constant velocity of 20 m/s, so it travels a distance of (20 m/s)(4 s) = 80 m. Therefore, the total distance traveled is 320 m + 240 m + 80 m = 640 m. The answer is C).

The Graph Shows the Velocity of a Particle as a Function