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

By using the area under the acceleration-time graph, we can find the change in velocity of the particle. From 0 to 5 seconds, the area under the acceleration-time graph is a trapezoid with height 7 m/s$^2$ and bases of 5 s and 2 s:
$$	ext{Area} = \frac{1}{2}(7	ext{ m/s}^2)(5	ext{ s}+2	ext{ s}) = 24.5	ext{ m/s}$$
Therefore, the change in velocity of the particle is +24.5 m/s (since the acceleration is in the positive x direction). The final velocity of the particle is:
$$	ext{Final velocity} = 	ext{Initial velocity} + 	ext{Change in velocity} = 15	ext{ m/s} + 24.5	ext{ m/s} = \boxed{	extbf{(C) }+30	ext{ m/s}}$$

At T = 0, a Particle Is Located at X