A body oscillates with simple harmonic motion along the x axis. Its displacement varies with time according to the equation x = 5.0 sin (πt + π/3). The velocity (in m/s) of the body at t = 1.0 s is
A) +7.9
B) −7.9
C) −14
D) +14
E) −5.0

Question

Quizplus · Accepted Answer

The velocity of a body in simple harmonic motion is found by differentiating the displacement equation with respect to time. Given x = 5.0 sin(πt + π/3), the velocity v = dx/dt = 5.0π cos(πt + π/3). At t = 1.0 s, v = 5.0π cos(π(1) + π/3) = 5.0π cos(4π/3) = 5.0π * (-1/2) = -5π ≈ -7.9 m/s.

A Body Oscillates with Simple Harmonic Motion Along the X