Formula
The energy of a body in motion equals half the product of mass and the square of speed: E = mv² / 2.
ENT-level problem
A body of mass $m = 1$ kg slides down a slope of height $h = 5$ m without friction. Find the speed of the body at the bottom of the slope. The acceleration due to gravity is $g = 10$ m/s²; neglect air resistance.
There is no friction, so the kinetic energy at the bottom equals the potential energy at the top:
$$mgh = \frac{mv^2}{2}$$
The mass cancels, hence
$$v = \sqrt{2gh} = \sqrt{2 \cdot 10 \cdot 5} = \sqrt{100} = 10 \text{ m/s}$$
The kinetic energy of a ball depends on its speed v. As the ball rolls down the hill, its speed increases and the kinetic energy grows at the expense of the potential energy.
The energy depends on the square of the speed: double the speed and the energy grows fourfold. A body at rest (v = 0) has no kinetic energy.
It is proportional to the square of the speed: double the speed and the energy quadruples.
No: at v = 0 the kinetic energy is zero. It appears only when the body moves.
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