At t=0, a particle starts from (−1,0) and moves towards positive x−axis with speed of v=3t2+2tm/s. The final position of the particle and the distance travelled by the particle respectively, as a function of time are
A
t3−t2−1m,t3−t2m
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B
t3−t2+1m,t3−t2m
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C
t3+t2−1m,t3+t2m
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D
t3−t2+1m,t3+t2m
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Solution
The correct option is Ct3+t2−1m,t3+t2m Given, particle starts from (−1,0), so the initial position of the particle is xi=−1
As we know that, ∫dx=∫t0v(t)dt ⇒∫xfxidx=∫t0(3t2+2t)dt ⇒(xf−xi)=[t3+t2]t0 ⇒xf+1=t3+t2⇒xf=t3+t2−1m
And, the distance travelled by the particle is given by ∫t0v(t)dt=∫t0(3t2+2t)dt=[t3+t2]t0=t3+t2m