If the velocity of a particle is given by v(t) = 7; [0, 5] the displacement is
A) 94.5
B) -35
C) 49
D) 35
E) 25

Question

Quizplus · Accepted Answer

The displacement can be found by taking the integral of the velocity function:
s(t) = ∫v(t)dt = ∫7 dt = 7t + C
To find the constant, we use the initial condition s(0) = 0:
0 = 7(0) + C
C = 0
Thus, the displacement over the interval [0,5] is:
s(5) - s(0) = 7(5) + 0 - (7(0) + 0) = 35. Therefore, the answer is D.

If the Velocity of a Particle Is Given by V(t)