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Question

If the displacement, velocity and acceleration of a particle at time t be x, v and f respectively, then which one is true?

A
f=v3d2tdx2
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B
f=v3d2tdx2
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C
f=v2d2tdx2
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D
f=v2d2tdx2
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Solution

The correct option is B f=v3d2tdx2
We know that the velocity can be written as:
v=dxdt

Therefore, 1v=dtdx

Now, expressing f in terms of velocity.

d2tdx2=d(dtdx)dx=d(1v)dx=1v2dvdt×1v
f=v3d2tdx2

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