Final answer:
The speed at which the house cat will have 20 J of kinetic energy is v √2, where v is the initial velocity.
Step-by-step explanation:
A student asked at what speed a house cat that initially has 10 J of kinetic energy at speed v will have 20 J of kinetic energy. To answer this, we can apply the kinetic energy formula:
Ke = 0.5 × m × v^2
We see that if the kinetic energy is doubling from 10 J to 20 J, the velocity must ×√2 because kinetic energy is proportional to the square of the velocity. Therefore, if the initial velocity is v, the new velocity v' needed to have 20 J of kinetic energy would be:
v' = v × √2