Question

A particle moves along the x-axis with position function x(t)=4sin(π−t/2) for 0≤t≤4π where t is measured in seconds. For what values of t does the particle have an acceleration of 0?

Answer 1

C

Explanation:

To find the values of t for which the particle has an acceleration of 0, we need to find the times when the derivative of the position function, which represents the particle's velocity, is equal to 0.

The position function of the particle is x(t) = 4sin(π-t/2). The derivative of this function is:

x'(t) = 4cos(π-t/2) * (-1/2)

= -2cos(π-t/2)

We can find the values of t for which the derivative is equal to 0 by setting x'(t) equal to 0 and solving for t:

-2cos(π-t/2) = 0

cos(π-t/2) = 0

π-t/2 = π/2 + nπ

t/2 = nπ

t = nπ

where n is an integer.

Therefore, the values of t for which the particle has an acceleration of 0 are t = 0, t = π, t = 2π, etc. These values occur at regular intervals of π seconds.