Acceleration of the particle in a rectilinear motion is given as a=3t2+4t−3 in (m/s2). The velocity of the particle as a function of time t is (Given, at t=0,u=1m/s)
A
t3+2t2−3t
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B
t3+t2−3t+1
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C
t3−2t2−3t
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D
t3+2t2−3t+1
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Solution
The correct option is Dt3+2t2−3t+1 Given, a(t)=3t2+4t−3 As we know that the velocity as a fuction of time is given by ∫vudv=∫t0(3t2+4t−3)dt ⇒[v]vu=[t3+2t2−3t]t0 ⇒v−u=t3+2t2−3t Or, ⇒v−1=t3+2t2−3t⇒v(t)=t3+2t2−3t+1