If a particle is moving such that the velocity acquired is proportional to the square root of the distance covered, then its acceleration is

Options

A. a constant
B. `prop s^(2)`
C. `prop(1)/(s^(2))`
D. `prop s`

Answer

A

Explanation

Let v be the velocity of the particle when the distance covered is s. Then,
`v prop sqrt(s)` [Given]
`implies v = lambda sqrt(s)`
`implies (dv)/(ds)=(lambda)/(2sqrt(s))`
`implies v(dv)/(ds)=(lambdav)/(2sqrt(s)) = (lambda^(2))/(2)` = constant.
Hence, the acceleration is constant.