1
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Question

# The acceleration 'a' in m/s2 of a particle is given by a a=3t2+2t+2 where t is the time. If the particle starts out with a velocity u = 2m/s at t=0, then the velocity at the end of 2 second is

A
12m/s
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B
18m/s
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C
27m/s
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D
36m/s
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Solution

## The correct option is B 18m/sWe have, a=dVdtGiven a=3t2+2t+2dV=a×dtdV=(3t2+2t+2)dtIntegrating bothe sides, we getV=3×t33+2t22+t=t3+t2+2t+C .....(1)where C is constantPutting t=0 in equation (1), we get2=0+CThen,C=2Substituting the value in equation (2), we getV=t3+t2+2t+2At t=2V=8+4+4+2=18m/s

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