Question

Find the derivative of r(t) = .

Answer 1

To find the derivative of the position function, take the derivative of the magnitude of the position using the chain rule. Use the second expression for centripetal acceleration.

Step-by-step explanation:

The problem is asking for the derivative of the position function r(t) = . To find this derivative, we need to take the derivative component by component with respect to time. Since the radius is a constant, the derivative of the position function is simply the derivative of the magnitude of the position.

Using the chain rule, we have:

• dr/dt = d/dt(sqrt(r(t)²)) = (1/2)(2r(t))(dr/dt)

Since r is given, we can use the second expression in the equation for centripetal acceleration:
ac = r(d²θ/dt²).