A) a constant
B) \[\propto {{s}^{2}}\]
C) \[\propto \frac{1}{{{s}^{2}}}\]
D) \[\propto \frac{1}{s}\]
Correct Answer: A
Solution :
Let v be the velocity of the particle when the distance covered is\[s\]. Then, \[v\propto \sqrt{s}\] (given) \[\Rightarrow \] \[v=\lambda \sqrt{s}\] \[\Rightarrow \] \[\frac{dv}{dx}=\frac{\lambda }{2\sqrt{s}}\] \[\Rightarrow \] \[v\frac{dv}{ds}=\frac{\lambda v}{2\sqrt{s}}=\frac{{{\lambda }^{2}}}{2}=\] \[\therefore \]The acceleration is constant.
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