Understanding the Relationship

* Direct Variation: This means the kinetic energy (KE) is proportional to the square of the velocity (v). We can write this as: KE = kv² where 'k' is a constant of proportionality.

Solving the Problem

1. Find the constant 'k':

* We know KE = 180 units when v = 60 mph.

* Substitute these values into the equation: 180 = k(60)²

* Solve for 'k': 180 = 3600k => k = 180/3600 = 1/20

2. Calculate KE at 20 mph:

* Now we know k = 1/20.

* Substitute v = 20 mph into the equation: KE = (1/20)(20)²

* Calculate: KE = (1/20)(400) = 20 units

Answer: The car has a kinetic energy of 20 units when traveling at 20 mph.