Question

question 13 of 27
a car has a mass of 8000 kg and a kinetic energy of 24,000 j. what is its speed?

a. 3 m/s
b. 1.7 m/s
c. 6 m/s
d. 2.4 m/s

Explanation:

Step1: Recall kinetic - energy formula

The formula for kinetic energy is $K = \frac{1}{2}mv^{2}$, where $K$ is kinetic energy, $m$ is mass, and $v$ is speed. We need to solve for $v$.

Step2: Rearrange the formula for $v$

Starting from $K=\frac{1}{2}mv^{2}$, we first multiply both sides by $2$ to get $2K = mv^{2}$. Then divide both sides by $m$: $v^{2}=\frac{2K}{m}$. Taking the square - root of both sides gives $v=\sqrt{\frac{2K}{m}}$.

Step3: Substitute the given values

We are given that $K = 24000\ J$ and $m = 8000\ kg$. Substituting these values into the formula $v=\sqrt{\frac{2K}{m}}$, we have $v=\sqrt{\frac{2\times24000}{8000}}=\sqrt{\frac{48000}{8000}}=\sqrt{6}\approx 2.4\ m/s$.

Answer:

D. $2.4\ m/s$