Question

A particle of mass m moves on a straight line with its velocity varying with the distance travelled according to the equation v = a$\sqrt{x}$, where 'a' is a constant.Find the total work done by all the forces during a displacement from x = 0 to x = d.

• A.
• B.
• C.
• D. none of these

Answer 1

The correct option is B

We know sum of work done by all the forces will be $\Delta$ K.E.

$W_{Net}=\Delta K.E$

I know K.E = $\frac{1}{2}m{v}^2$

Where v = a$\sqrt{x}$

At x = 0

v = 0 K.E = 0

At x = d

v =a$\sqrt{d}$ K.E = $\frac{1}{2}m{a}^{2}d$

$\Delta K.E=\frac{1}{2}m{a}^{2}d$

$\Rightarrow W_{net}=\frac{1}{2}m{a}^{2}d$