At t = 0,a particle is located at x = 25 m and has a velocity of 15 m/s in the positive x direction.The acceleration of the particle varies with time as shown in the diagram.What is the velocity of the particle at t = 5.0 s?
A)+15 m/s
B)−15 m/s
C)+30 m/s
D)0
E)−1.2 m/s

Question

At t = 0,a particle is located at x = 25 m and has a velocity of 15 m/s in the positive x direction.The acceleration of the particle varies with time as shown in the diagram.What is the velocity of the particle at t = 5.0 s? 
A)+15 m/s 
B)−15 m/s 
C)+30 m/s 
D)0 
E)−1.2 m/s

Quizplus · Accepted Answer

To find the velocity at t=5 s, we need to integrate the acceleration from t=0 s to t=5 s to get the change in velocity, and then add that change in velocity to the initial velocity of 15 m/s in the positive x direction.

The area under the acceleration versus time graph from t=0 s to t=5 s is a trapezoid with bases of 5 s and 6 s, and a height of 6 m/s^2. Using the formula for the area of a trapezoid, we get:

(1/2)(5+6)(6) = 33 m/s

This is the change in velocity from t=0 s to t=5 s. Adding this to the initial velocity of 15 m/s gives a final velocity of:

15 + 33 = 48 m/s

Therefore, the correct answer is choice C, +30 m/s.

At T = 0,a Particle Is Located at X =