Question

If velocity of a particle at a position os given as $v^2=2x$, then the acceleration of particle is [where $x$ is metre and $v$ in m/s]

• A. $4m/s^2$
• B. $0.5m/s^2$
• C. $2m/s^2$
• D. $1m/s^2$

Answer 1

The correct option is D $1m/s^2$

Given,

The velocity of a particle at a position is given a

$v^2=2x$. . . . . . . . . . . .. . .. (1)

Acceleration, $a=v\frac{dv}{dx}$. . . . . . . .(2)

Differentiate equation (1) with respect to $x$,

$\frac{d\left(v^2\right)}{dx}=2\frac{d\left(x\right)}{dx}$

$2v\frac{dv}{dx}=2\times 1$

$v\frac{dv}{dx}=1$. . . . . . . . . . .(3)

From equation (2) and (3), we get

$a=1m/s^2$

The correct option is D.