The velocity of the particle is given by v=3t2+2t in m/s. The acceleration and displacement of the particle as a function of time respectively are
A
(t+2)m/s2,(3t3+t2)m
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B
(6t+2)m/s2,(t3+t2)m
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C
(6t2+2)m/s2,(t3+t2)m
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D
(t+2)m/s2,(t3+t)m
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Solution
The correct option is B(6t+2)m/s2,(t3+t2)m Given, v(t)=3t2+2t As we know that acceleration of the particle is given by a(t)=dvdt=d(3t2+2t)dt=(6t+2)m/s2 Also, v=dxdt⇒x(t)=∫t0v(t)dt ⇒x(t)=∫t0(3t2+2t)dt ⇒x(t)=(t3+t2)m