Question

2 multiple choice 1 point
select the correct equation for kinetic energy.
(1/2)mv²
mg
(1/2)mv
m²v²
3 multiple choice 1 point
select the correct equation for potential energy.
mg
mv²
ma
mgh

Explanation:

• Kinetic energy is the energy of motion. The formula \(KE=\frac{1}{2}mv^{2}\) (where \(m\) is mass and \(v\) is velocity) is derived from work - energy principles. For example, when a force \(F = ma\) (using \(a=\frac{v - u}{t}\) and \(s=\frac{u + v}{2}t\)) acts over a distance \(s\) to accelerate an object from rest (\(u = 0\)), the work done \(W=Fs=mas=m\frac{v}{t}\times\frac{v}{2}t=\frac{1}{2}mv^{2}\), which is the kinetic energy.
• Potential energy (gravitational potential energy near the Earth's surface) is given by \(PE = mgh\) (where \(m\) is mass, \(g\) is the acceleration due to gravity, and \(h\) is height). It represents the energy stored in an object due to its position in a gravitational field. The force of gravity \(F = mg\), and the work done in lifting an object to a height \(h\) is \(W=Fh=mgh\), which is the gravitational potential energy.

Answer:

1. \((1/2)mv^{2}\)
2. \(mgh\)