Distance, Velocity, Acceleration, and Rectilinear

Question

A particle moves along the x-axis so that at any time t, measured in seconds, its position is given by s(t) = 5cos(t) - sin(3t), measured in feet. What is the acceleration of the particle at time t = π seconds?

Answer 1

s(t) = 5cos(t) - sin(3t)

v(t) = s'(t) = 5·[-sin(t)] - cos(3t)·d/dt(3t) = -5sin(t) - 3cos(3t)

a(t) = v'(t) = s''(t) = -5cos(t) - 3·[-sin(3t)]·d/dt(3t) = -5cos(t) + 9sin(3t)

For t = ∏

a(∏) = -5cos(∏) + 9sin(3∏) = -5(-1) + 9(0) = 6

The acceleration of the particle is 6 ft/s²