Question

An object of mass \(0.12 \mathrm{kg}\) is moving at $1.80 \times 10^{8} \mathrm{m} / \mathrm{s}$ What is its kinetic energy in joules?

Short answer

Answer: The kinetic energy of the object is 1.944 x 10^15 joules.

Step-by-step solution

Write down the kinetic energy formula

Firstly, we must write down the formula we need to calculate the kinetic energy: \(K.E. = \frac{1}{2}mv^2\)

Plug the given values into the formula

Now that we have the formula, we can plug in the given values for mass and velocity: \(K.E. = \frac{1}{2}(0.12 kg)(1.80 \times 10^8 m/s)^2\)

Calculate the square of velocity

Before we proceed, we will calculate the square of the given velocity: \((1.80 \times 10^8 m/s)^2 = (1.80^2) \times (10^8)^2 = 3.24 \times 10^{16} m^2/s^2\)

Finish the calculation

Now, we can substitute the value calculated in the previous step into the kinetic energy formula and find the answer: \(K.E. = \frac{1}{2}(0.12 kg)(3.24 \times 10^{16} m^2/s^2)\) \(K.E. = 0.06 kg \times 3.24 \times 10^{16} m^2/s^2\) Finally, we can calculate the kinetic energy: \(K.E. = 1.944 \times 10^{15} J\) The kinetic energy of the object is \(1.944 \times 10^{15}\) joules.