Question

An object is found to rotate with an angular velocity $\omega \left(t\right)=5t+3$, where $\omega$ is measured in radians per second. The initial angular displacement of the object is zero.
Which of the following best corresponds to the angular displacement of the object after $5$ seconds?

• A. $28rad/s$
• B. $77.5rad$
• C. $5rad/s$
• D. $25rad/s$
• E. $50rad/s$

Answer 1

Answer: (B)

$77.5rad$

Angular velocity of rotation $w\left(t\right)=5t+3$ rad/s

Integrating w.r.t time we get angular displacement ${\int }_0^{\theta }\theta ={\int }_0^{5}w\left(t\right)dt$

$\therefore$ ${\int }_0^{\theta }\theta ={\int }_0^5(5t+3)dt$

OR $\theta =(\frac{5t^2}{2}+3t){|}_0^5$

OR $\theta =\frac{5\times 5^2}{2}+3\times 5-0=77.5$ radian