Problem

A block at the end of a spring is stretched past its rest position and released. Its position at time t is given by the formula d(t) = 4cos(t). Find the velocity of the spring at time t. When does the block move fastest?

Solution

Here's a graph of the position function. Click here to see a movie of the block.

The velocity function for the block at time t is the derivative of the position function.

The block is moving the fastest when the magnitide of the velocity is greatest. Since |sin(t)| attains its maximum values when t is p/2, 3p/2, 5p/2, and so on, the block will be moving fastest when t equals