Question

A rocket-powered car is set inside a circular track and ignited. Pressure sensors on the wall of the track measure the centripetal acceleration a of the car as a function of time t to be ac (t) = h²t⁴ + 2hnt²+ n²

where h and n are constants. If the radius of the track is d, what is the tangential acceleration at of the rocket as a function of time t?

Answer 1

The tangential acceleration of the rocket can be found by taking the derivative of the speed function with respect to time.

Step-by-step explanation:

The tangential acceleration of the rocket can be found by taking the derivative of the speed function with respect to time. In this case, the speed function is given by |v(t)|, where v(t) represents the velocity of the rocket at time t. The magnitude of the tangential acceleration, at, is the time derivative of |v(t)|.

Using Equation 4.31, we can calculate the magnitude of the tangential acceleration as:

at(t) = |dv(t)/dt|

Evaluating this expression at t = 2.0 s will give us the tangential acceleration of the rocket at that time.