If a point is moving in a line so that its velocity at time tis proportional to the square of the distance covered, then its acceleration at time t varies as

A
cube of the distance
B
the distance
C
square of the distance
D
none of these

Solution:

Lets be the distance covered in time t. Then,

$\begin{array}{l} \frac{d s}{d t} = k s^{2} \\ \Rightarrow \frac{d^{2} s}{d t^{2}} = 2 k s \frac{d s}{d t} = 2 k s \times k s^{2} = 2 k^{2} s^{3} \end{array}$

$\Rightarrow {Acc}^{n} \propto (Distance)^{3}$

Solution:

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