Question

An object oscillates in the x direction with a position of x(t) = 3cos(2πt), where distance is measured in meters and time is measured in seconds. what is the speed of the object at t=1s?

Answer 1

For this case we have the following position equation:
x (t) = 3cos (2πt)
Deriving to obtain the speed we have:
x '(t) = -3 * 2 * π * sine (2πt)
Substituting for t = 1 we have:
x '(1) = -3 * 2 * π * sine (2π (1))
Rewriting:
x '(1) = -6πsine (2π)
x '(1) = -6π (0)
x '(1) = 0
Answer:
The speed of the object at t = 1s is:
x '(1) = 0 m / s