The angular position of a point on the rim of a 28.3 cm rotating wheel is given by (t) = 3.3 t2 ' 6.5 t +6.4, where is measured in radians and t is measured in seconds.

What is the instantaneous angular acceleration of the point at time t = 4.5 s?
What is the instantaneous tangential (not radial!) acceleration a of the point at time t =4.5 s?
What is the instantaneous angular velocity of the point at time t = 7.5 s?
What is the instantaneous speed v of the point at time t = 7.5 s?
What is the average angular speed av of the point over the time interval starting time t = 4.5 s and ending at the time t = 7.5 s?
Through what angular displacement does the wheel turn during this time?

Substitute t in the given equation to get the position of the point.

Get the derivative of the function to get the equation for the velocity of the point at time t.

Get the second derivative of the function to get the equation for the acceleration of the point at time t.

Tangential acceleration is given by the formula: a = \frac{v^2}{r}

Angular velocity is given by: \omega = \frac{v}{r}

Average speed = Total distance / Total time

Use s = r\theta