Question

A wheel has a constant angular acceleration of
3.0 rad/s2, During a certain 4.0 s interval, it turns
through an angle of 120 rad. Assuming that at
t = 0, angular speed 0. = 3 rad/s how long, is
motion at the start of this 4.0 second interval ?
(1) 7 sec.
(2) 9 sec.
(3) 4 sec.
(4) 10 sec.​

Answer 1

9 seconds is the answer

Answer 2

ANSWER:

(1) It takes 7 seconds.

EXPLANATION:

The angular acceleration of the wheel is given by \alpha=3

The time it takes to turn an angle of 120 rad  

The time taken to turn an angle of 120 rad is 4 seconds

Let us find the angular velocity in the time interval of 4 sec.

The value of angular velocity is  

$\alpha=\frac{\omega}{t}$

$3 \times 4=\omega$

$\omega=12 r a d / \mathrm{sec}$

Therefore, the time of the motion required is  

$\omega=\omega^{\prime}+\alpha t$

$24=3+3 \times t$

$21 / 3=t$

$7 \sec =t$

Therefore, the time required to start motion after 4 seconds interval is 7 sec