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Question

If motion of a particle is represented by s=et+4tcost, then the acceleration of the particle at any time t is
[Hint: Acceleration of the particle is d2sdt2]

A
et4tln4+cost
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B
et+4t(ln4)2+cost
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C
et+4t(ln4)2cost
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D
et+4tln4+cost
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Solution

The correct option is B et+4t(ln4)2+cost
As we know that the acceleration of the particle at any time t is given by
d2sdt2 d(dsdt)dt
Given, S=et+4tcost
So, we have dsdt=d(et+4tcost)dt
detdt+d4tdtdcostdt=et+4tln4+sint
Thus, d2sdt2=d(et+4tln4+sint)dt
detdt+ln4d4tdt+dsintdt=et+4t(ln4)2+cost

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