Question

What's the impulse of a *thing* if it's mass is 1kg and it's kinetic energy is 8J?

Answer 1

Let's first find the velocity of the *thing* from the definition of the kinetic energy:

$$KE=\dfrac{1}{2}mv^2,$$ $$v=\sqrt{\dfrac{2KE}{m}}.$$

Finally, we can find the impulse of the *thing*:

$$J=\Delta p=mv=m\sqrt{\dfrac{2KE}{m}}=\sqrt{2mKE},$$ $$J=\sqrt{2mKE}=\sqrt{2\cdot1\ kg\cdot8\ J}=4\ N\cdot s.$$