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Question

Acceleration of the particle in a rectilinear motion is given as a=2t2 in (m/s2). The final position of the particle as a function of time t is
(Given that at t=0,u=2 m/s,x=4 m)

A
t33t2+2t+4
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B
t33t2+2t
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C
t33t2+4
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D
t33t2
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Solution

The correct option is A t33t2+2t+4
Given, a(t)=2t2
As we know that the velocity as a fuction of time is given by
vudv=t0(2t2)dt
[v]vu=[t22t]t0
vu=t22t
Or, v2=t22t v(t)=t22t+2
Now, final position of the particle is given as
xfxix(t)dt=t0v(t)dt=t0(t22t+2)dt
xfxi=[t33t2+2t]t0
xf4=[t33t2+2t]
xf(t)=[t33t2+2t+4]

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