Question

The kinetic energy E of an object (in joules) varies jointly with the object's mass m (in

kilograms) and the square of the object's velocity v (in meters per second). An object
with a mass of 8.6 kilograms and a velocity of 5 meters per second has a kinetic
energy of 752.5 joules.
Write an equation that relates E, m, and v.
Then use the equation to find the kinetic energy of an object with a mass of 2
kilograms and a velocity of 9 meters per second.

Answer 1

The equation that relates E, m, and v can be written as:

E = k * m * v^2

where k is the constant of proportionality.

To find the value of k, we can use the given information that an object with a mass of 8.6 kilograms and a velocity of 5 meters per second has a kinetic energy of 752.5 joules. Substituting these values into the formula, we get:

752.5 = k * 8.6 * 5^2

Simplifying and solving for k, we get:

k = 752.5 / (8.6 * 25) = 3.1

Therefore, the equation that relates E, m, and v is:

E = 3.1 * m * v^2

To find the kinetic energy of an object with a mass of 2 kilograms and a velocity of 9 meters per second, we can substitute these values into the equation:

E = 3.1 * 2 * 9^2 = 496.2 joules

Therefore, the kinetic energy of the object is 496.2 joules.