Final answer:
The wheel's point initially at the bottom has traveled through an angle of approximately 40425.8 degrees after 14 seconds, considering its constant angular acceleration and counterclockwise direction.
Step-by-step explanation:
The student's question is about calculating the angular displacement of a wheel after a certain period of time when the wheel starts from rest and has a constant angular acceleration. Given that the wheel has a diameter of 39 cm and an angular acceleration of 7.2 rad/s², we can find the angle through which a point on the edge of the wheel has traveled after 14 seconds by using the angular kinematic equation:
\( \theta = \omega_0 t + \frac{1}{2} \alpha t^2 \)
where:
- \( \theta \) = angular displacement in radians
- \( \omega_0 \) = initial angular velocity, which is 0 rad/s since it starts from rest
- \( \alpha \) = angular acceleration
- t = time in seconds
Plugging in the values, we get:
\( \theta = 0 \times 14 + \frac{1}{2} \times 7.2 \times 14^2 \)
\( \theta = \frac{1}{2} \times 7.2 \times 196 \)
\( \theta = 3.6 \times 196 \)
\( \theta = 705.6 \text{ rad} \)
To convert to degrees, we use the conversion factor where \( 1 \text{ rad} = \frac{180}{\pi} \text{ degrees} \).
\( \theta_{\text{degrees}} = 705.6 \times \frac{180}{\pi} \)
Then, the angle \