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Question

The displacement of the particle is given by x=3t3−2t2+5 in m. The acceleration of the particle at 4 sec is

A
58 m/s2
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B
62 m/s2
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C
68 m/s2
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D
70 m/s2
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Solution

The correct option is C 68 m/s2
As we know that the acceleration of the particle is given by
a=dvdt and also, v=dxdt
Given, x=3t32t2+5
So, v=dxdt=d(3t32t2+5)dt
v=9t24t
also, a=dvdt=d(9t24t)dt=18t4
Thus, the acceleration of the particle is 18×44=68 m/s2

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