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Question

Acceleration of the particle in a rectilinear motion is given as a=4t+3 in (m/s2). The velocity and displacement as a function of time t respectively are
(Given that at t=0,u=3 m/s,x=0 m)

A
(t2+3),(t33+3t22+3t)
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B
(t2+3t),(t33+3t22)
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C
(2t2+3t+3),(2t33+3t22+3t)
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D
(2t2+3t),(2t33+3t22)
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Solution

The correct option is C (2t2+3t+3),(2t33+3t22+3t)
Given, a(t)=4t+3
As we know that the velocity as a fuction of time is given by
vudv=t0(4t+3)dt
[v]vu=[2t2+3t]t0
vu=2t2+3t
Or, v3=2t2+3t v(t)=2t2+3t+3
Now, displacement is given by
x(t)=t0v(t)dt=t0(2t2+3t+3)dt
x(t)=[2t33+3t22+3t]t0
x(t)=[2t33+3t22+3t]

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