Kinetic energy and speed

Trolleys of $1\ \text{kg}$, $2\ \text{kg}$ and $4\ \text{kg}$ move at speeds from $0\ \text{m/s}$ to $10\ \text{m/s}$. You will make the program find their kinetic energy, check the doubling rule, and work back from an energy to a speed. Then it draws the three curves.

The idea. $KE = \tfrac{1}{2}mv^2$: twice the speed gives four times the energy, and $v = \sqrt{\dfrac{2KE}{m}}$.

Your tasks.

1. Inside the loop, work out KE for the mass m at the speed v, in joules.
2. Find ratio: the energy of the $2\ \text{kg}$ trolley at $6\ \text{m/s}$, divided by its energy at $3\ \text{m/s}$.
3. Find speed, the speed at which the $2\ \text{kg}$ trolley has $100\ \text{J}$, in m/s.