Question

the velocity of a 10.0 kg object that has 720 j of kinetic energy is \boxed{} m/s. (report the answer to two significant figures.)

Explanation:

Step1: Recall the kinetic energy formula

The formula for kinetic energy ($KE$) is $KE = \frac{1}{2}mv^2$, where $m$ is the mass of the object and $v$ is its velocity. We need to solve for $v$. Rearranging the formula to solve for $v$: first, multiply both sides by 2 to get $2KE = mv^2$, then divide both sides by $m$ to obtain $v^2=\frac{2KE}{m}$, and finally take the square root of both sides: $v = \sqrt{\frac{2KE}{m}}$.

Step2: Substitute the given values

We know that $KE = 720\ J$ and $m = 10.0\ kg$. Substituting these values into the formula for $v$: $v=\sqrt{\frac{2\times720}{10.0}}$.

Step3: Calculate the value inside the square root

First, calculate the numerator: $2\times720 = 1440$. Then divide by the mass: $\frac{1440}{10.0}=144$.

Step4: Take the square root and round

Now, take the square root of 144: $\sqrt{144} = 12$. Since we need to report the answer to two significant figures, and 12 already has two significant figures, the velocity is $12\ m/s$.

Answer:

12