Question

When the red light turns green at an intersection, you step on the accelerator andyour car begins moving (it was initially at rest). Suppose the angular acceleration ofthe wheels of the car is 6.8 rad/s2. If the car accelerates for 25 seconds, what is theresulting angular displacement? Give your answer in radians

Answer 1

Given data

The angular acceleration of the car is

$\alpha=6.8rad/s^2$

The given time is t = 25 s

The expression for the angular displacement is given by the rotational equation of motion as

$\theta=\frac{1}{2}\alpha t^2$

Substitute the values in the above expression as

$\begin{gathered} \theta=\frac{1}{2}(6.8)(25)^2 \\ =2125\text{ rad} \end{gathered}$