Mathematics

Instantaneous velocity is the rate of change of position—you find it by taking the derivative of the displacement function with respect to time. Since $x(t)$ is given as a sine function, you'll differentiate it using the chain rule, then evaluate at the specific time. The key is remembering that the derivative of $\sin(u)$ is $\cos(u) \cdot \frac{du}{dt}$.

Instantaneous velocity is the rate of change of position—you find it by taking the derivative of the displacement function with respect to time. Since $x(t)$ is given as a sine function, you'll differentiate it using the chain rule, then evaluate at the specific time. The key is remembering that the derivative of $\sin(u)$ is $\cos(u) \cdot \frac{du}{dt}$.