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
