Show that the units of kinetic energy (from ½ mv2 ) and gravitational potential energy (from mgh) are the same.

The units of both types of energy are Joule (kg × m² × s⁻²).

Explanation:

Step 1: Show the units of kinetic energy

The equation for kinetic energy is:

K = 1/2 × m × v²

where,

m: mass

v: speed

The units are:

K = 1/2 × m × v²

[K] = kg × (m/s)²

[K] = kg × m² × s⁻² = J

Step 2: Show the units of gravitational potential energy

The equation for gravitational potential energy is:

G = m × g × h

where,

m: mass

g: gravity

h: height

The units are:

G = m × g × h

[G] = kg × m/s² × m

[G] = kg × m² × s⁻² = J

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