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Question

A car wheel rotates with an angular acceleration α=4t3(in rad/s2) where t is the time taken (in seconds). If the wheel has initial angular velocity ω0=20 rad/s, then the angular velocity ω(t) after 2 s is

A
20 rad/s
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B
36 rad/s
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C
4 rad/s
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D
16 rad/s
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Solution

The correct option is B 36 rad/s
Initial angular velocity w0=20 rad/s
Given α=4t3
α is a function of time
dωdt=4t3
dω=4t3dt
Integrating on both sides, ωω0dω=t04t3dt
ωω0=[t4]20
ω=ω0+[t4]20
=20+16=36 rad/s

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