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Let's Play

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A child's top is spun with angular acceleration \( \alpha=4 t^{3}-3 t^{2}+2 t \) where \( t \) is in
\( \mathrm{P} \) seconds and \( \alpha \) is in radians per secondsquare. At \( t=0 \), the top has angular velocity \( \omega_{0}=2 \mathrm{rad} / \mathrm{s} \) and a reference line on it is at an angular position \( \theta_{0}=1 \mathrm{rad} \)
Statement I: Expression for angular velocity
\[
\omega=\left(2+t^{2}-t^{3}+t^{4}\right) \mathrm{rad} / \mathrm{s}
\]
Statement II: Expression for angular position
\[
\theta=\left(1+2 t-3 t^{2}+4 t^{3}\right) \mathrm{rad}
\]
(1) Only statement-I is true
(2) Only statement-II is true
(3) Both of them are true
(4) None of them are true
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