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

At t=0, velocity of the particle is 15 m/s in the positive x direction. As acceleration is positive for the first 4 seconds, the velocity of the particle will keep on increasing. At t=4 s, the velocity of the particle will be v = u + at = 15 + (2)(4) = 23 m/s in the positive x direction.

From t=4 s to 5 s, the acceleration is negative. As the velocity is in the positive x direction, the negative acceleration will slow the particle down. The change in velocity over that 1 second is:
Δv = at = (−2)(1) = −2 m/s

Therefore, the final velocity at t = 5.0 s is:
v = u + Δv = 23 − 2 = 21 m/s in the positive x direction.

Thus, the correct answer is (C)+30 m/s.

At T = 0, a Particle Is Located at X