Question

An amount of work W is done on an object of mass m initially at rest, and as result it winds up moving at speed v. Suppose instead it were already moving at speed v and the same amount of work W was done on it. What would be its final speed

Answer 1

Answer:

Explanation:

Given

W amount of work is done on the system such that it acquires v velocity after operation(initial velocity)

According to work energy theorem work done by all the forces is equal to change in kinetic energy of object

$W=\frac{1}{2}mv^2---1$

where m=mass of object

v=velocity of object

When the object is already have velocity v then the final speed is given by work energy theorem

$W=\frac{1}{2}mv_f^2-\frac{1}{2}mv^2-----2$

From 1 and 2 we get

$\frac{1}{2}mv^2=\frac{1}{2}mv_f^2-\frac{1}{2}mv^2$

$2\times \frac{1}{2}mv^2=\frac{1}{2}mv_f^2$

$v_f^2=2v^2$

$v_f=\sqrt{2}v$