Question

A ball is spun with angular acceleration $\alpha =6t^2-2t$ where $t$ is in second and $\alpha$ is in rads ${}^{-2}.$ At $t=0$, the ball has angular velocity of $10$ rads ${}^{-1}$ and angular position of $4rad$. The most appropriate expression for the angular position of the ball is:

• A. $\frac{3}{2}{t}^4-t^2+10t$
• B. $\frac{t^4}{2}-\frac{t^3}{3}+10t+4$
• C. $\frac{2t^4}{3}-\frac{t^3}{6}+10t+12$
• D. $2t^4-\frac{t^3}{2}+5t+4$

Answer 1

Answer: (B)

$\frac{dw}{dt}=6t^2-2t$
$\underset{10}{\overset{w}{\int }}dw=2t^3-t^2$
$w=10+2t^3-t^2$
$\frac{d\theta }{dt}=10+2t^3-t^2$
$\underset{4}{\overset{\theta }{\int }}d\theta =10+2t^3-t^2$
$\theta =4+10t+\frac{t^4}{2}-\frac{t^3}{3}$