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 WITH, suppose the object’s final speed is v. What will be the object’s final speed if you do twice as much work?1. 4 v2. 2 v3. still v4. v/25. v.2

Answer 1

Answer:

v_{f2} = √ 2 v_{f}

Explanation:

Work and kinetic energy are related by

       W = ΔK

The formula for work is

    W = F . d

The formula for kinetic energy is

      K = ½ m v²

     W = $K_{f}$ - K₀

Since the body starts from rest, the initial velocity is ro and therefore the kinetic energy is zero.

       W = K_{f}

       W = ½ m v_{f}²

       v_{f} = √ 2W / m

       

    If  W = 2 W₀

       v_{f2} = √ 2 (2W₀) / m

       v_{f2} = √ 2  √2W₀ / m

       v_{f2} = √ 2 v_{f}