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Question

Acceleration of the particle in a rectilinear motion is given as a=2t6 in (m/s2). The displacement as a function of time t respectively is
(Given, at t=0,u=2 m/s,x=2 m)

A
2t333t2+2t+2
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B
t333t2+2t
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C
t333t2+2t+2
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D
t333t2
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Solution

The correct option is B t333t2+2t
Given, a(t)=2t6
As we know that the velocity as a fuction of time is given by
vudv=t0(2t6)dt
[v]vu=[t26t]t0
vu=t26t
v2=t26t v(t)=t26t+2
Now, displacement is given by
x(t)=t0v(t)dt=t0(t26t+2)dt
x(t)=[t333t2+2t]t0
x(t)=(t333t2+2t)

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