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?

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