Question

A particle moves in a straight line in such a way that its velocity at any point is given by $v^2=2-3x$, where $x$ is measured from a fixed point. The acceleration is

• A. uniform
• B. zero
• C. non-uniform
• D. indeterminate

Answer 1

The correct option is A uniform

We know that acceleration is nothing but the time derivative of velocity $v$ so differentiating the expression $v^2=2-3x$ with respect to $t$

we get $2v\frac{dv}{dt}=0-3\frac{dx}{dt}=0-3v=-3v$ ........................... 1

because $dx/dt=velocity=v$

Solving equation-1 , we get $v(\frac{2dv}{dt}+3)=0$ or $\frac{2dv}{dt}+3=0$ or $\frac{2dv}{dt}=-3$ or $\frac{dv}{dt}=-3/2$ which is a constant so acceleration is constant so uniform acceleration.