Question

Kinetic energy refers to the energy of an object in motion. The amount of energy an object has (K) is related to the mass of the object (m, measured in kg), and Its velocity (v, measured in m/s). The formula used to calculate kinetic energy is K = 4mv.

a) Solve for Kif m = 20 kg and v = 18 m/s.
b) Solve for mif K = 486 and v = 9 m/s.
c) Solve for v if K = 345 and m = 7 kg.
Show all work for each question.

Answer 1

The kinetic energy of an object can be calculated using the formula KE = 1/2mv². Solving the provided problems, we find: a) K = 3240 Joules; b) m = 12 kg; c) v ≈ 9.93 m/s.

Step-by-step explanation:

Kinetic energy is the energy an object has due to its motion, and can be calculated using the formula KE = 1/2mv², where m is the mass in kilograms and v is the velocity in meters per second. In part a, to solve for the kinetic energy K when m = 20 kg and v = 18 m/s, we plug these values into the formula:

K = 1/2 × 20 kg × (18 m/s)² = 1/2 × 20 × 324 = 20 × 162 = 3240 Joules

In part b, to solve for the mass m when K = 486 Joules and v = 9 m/s, we rearrange the formula and solve for m:

m = (2K) / v² = (2 × 486) / (9²) = 972 / 81 = 12 kg

In part c, to solve for the velocity v when K = 345 Joules and m = 7 kg, we again rearrange the formula to solve for v:

v = √((2K) / m) = √((2 × 345) / 7) = √(690 / 7) = √98.57 ≈ 9.93 m/s