Question

An automobile with a mass of \(1600 \mathrm{kg}\) has a speed of $30.0 \mathrm{m} / \mathrm{s} .$ What is its kinetic energy?

Short answer

Answer: The kinetic energy of the automobile is 720,000 J.

Step-by-step solution

Identify the given values

Here, we are given the mass of the automobile, \(m = 1600 \mathrm{kg}\), and its speed, \(v = 30.0 \mathrm{m/s}\).

Write down the formula for kinetic energy

The formula for kinetic energy is given by: \(KE = \frac{1}{2}mv^2\).

Plug in the given values into the formula

Lets plug the given mass \(m\) and speed \(v\) into the formula of kinetic energy. Thereby, we can substitute \(m=1600\,\mathrm{kg}\) and \(v=30.0\,\mathrm{m/s}\): \(KE = \frac{1}{2} (1600\,\mathrm{kg}) (30.0\,\mathrm{m/s})^2\).

Perform the calculation

Now, let's calculate the kinetic energy: \(KE = \frac{1}{2} (1600\,\mathrm{kg}) (30.0\,\mathrm{m/s})^2 = 800\,\mathrm{kg}\cdot (900\,\mathrm{m^2/s^2}) = 720,\!000\,\mathrm{J}\).

State the final answer

The kinetic energy of the automobile is \(720,\!000\,\mathrm{J}\).