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Question

At t=0, a particle starts from (1,0) and moves towards positive xaxis with speed of v=3t2+2t m/s. The final position of the particle and the distance travelled by the particle respectively, as a function of time are

A
t3t21 m,t3t2 m
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B
t3t2+1 m,t3t2 m
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C
t3+t21 m,t3+t2 m
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D
t3t2+1 m,t3+t2 m
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Solution

The correct option is C t3+t21 m,t3+t2 m
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
(xfxi)=[t3+t2]t0
xf+1=t3+t2 xf=t3+t21 m
And, the distance travelled by the particle is given by
t0v(t)dt=t0(3t2+2t)dt=[t3+t2]t0=t3+t2 m

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