Question

a roller coaster car with a mass of 500 kg has 64,000 j of kinetic energy (ke). the speed (v) of the car is

Explanation:

Step1: Write the kinetic energy formula

The formula for kinetic energy is \(KE=\frac{1}{2}mv^{2}\), where \(m\) is the mass and \(v\) is the speed.

Step2: Rearrange the formula to solve for \(v\)

Starting with \(KE = \frac{1}{2}mv^{2}\), we can multiply both sides by \(2\) to get \(2KE=mv^{2}\). Then divide both sides by \(m\): \(v^{2}=\frac{2KE}{m}\). Finally, take the square - root: \(v=\sqrt{\frac{2KE}{m}}\).

Step3: Substitute the given values

Given \(m = 500\space kg\) and \(KE=64000\space J\). Substitute into the formula: \(v=\sqrt{\frac{2\times64000}{500}}\).
First, calculate the numerator \(2\times64000 = 128000\). Then \(\frac{128000}{500}=256\).

Step4: Calculate the square - root

\(v=\sqrt{256}\)

Answer:

\(16\space m/s\)