A particle moves along a line so that at time t, its position is s=4sin4t. What is the particle's maximum velocity?

Answer 1

The velocity of the particle is given by the derivative of its position function:
v(t) = 16cos(4t)

To find the maximum velocity, we need to find the maximum value of cos(4t). Since cos ranges from -1 to 1, its maximum value is 1. Therefore, the maximum velocity is:

v(max) = 16cos(0) = 16

So the particle's maximum velocity is 16.