Answer:
[tex]\theta=144\ rad[/tex]
Explanation:
given,
α=( 10+6 t ) rad/s²
[tex]\alpha =\dfrac{d\omega}{dt}[/tex]
[tex]d\omega= \alpha dt[/tex]
integrating both side
[tex]\omega= \int (10+6 t )dt[/tex]
[tex]\omega=10 t+6\dfrac{t^2}{2}[/tex]
[tex]\omega=10 t+3t^2[/tex]
we know
[tex]\omega =\dfrac{d\theta}{dt}[/tex]
[tex]d\theta= \alpha dt[/tex]
integrating both side
[tex]\theta= \int (10 t+3t^2 )dt[/tex]
[tex]\theta=10\dfrac{t^2}{2}+3\dfrac{t^3}{3}[/tex]
[tex]\theta=5 t^2+t^3[/tex]
now, at t = 4 s θ will be equal to
[tex]\theta=5\times 4^2+4^3[/tex]
[tex]\theta=144\ rad[/tex]
