If a=(3t2+2t+1)m/s2 is the expression according to which the acceleration of a particle moving along a straight line varies, then find displacement of the particle 2 seconds after starting.
A
26m
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B
263m
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C
307m
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D
267m
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Solution
The correct option is B263m a=(3t2+2t+1) ∫v0dv=∫t0(3t2+2t+1dt)(∵a=dvdt) v=t3+t2+t v=dsdt ds=vdt
Assume it will cover s displacement in 2 seconds. ∫s0ds=∫20(t3+t2+t)dt s=[t44+t33+t22]20 s=4+83+2 s=12+8+63=263m