Question

You do a certain amount of work on an object initially at rest, and all the work goes into increasing the object’s speed. If you do work W, suppose the object’s final speed is v. What will be the object’s final speed if you do twice as much work?

Answer 1

The final speed become
`√(2)` of the initial speed .

Step-by-step explanation:

We know that kinetic energy given as

`K.E.=(1)/(2)mv^2`

m=mass ,v=velocity

From work power energy theorem

Work done by all forces = Change in the kinetic energy

At initial condition

`W=(1)/(2)mv^2` --------1

Lets take the final speed is v' when the work done become 2W

`2W=(1)/(2)mv'^2` ---------2

From above two equation

`2* (1)/(2)mv^2=(1)/(2)mv'^2`

2 v² = v'²

Therefore we can say that

`v'=√(2) \ v`

The final speed become
`√(2)` of the initial speed .