Question
\begin{tabular}{l} The kinetic energy \( E \) \\ of a moving object is \\ given by \( E=\frac{1}{2} m v^{2} \), \\ where \( m \) is its mass in \\ kilograms and \( v \) is its \\ velocity in \\ meters/second. \\ Graph this equation \\ for a vehicle with a \\ mass of 800 kg using \\ a calculator or other \\ technology. \\ What is the velocity when the kinetic \\ energy is 160000 J? \\ Write all answers on the same line \\ separated by commas. \\ \( v= \) \\ \hline Fnter your next step here \\ \( m / s \)\end{tabular}
Ask by Elliott Lawson. in the United States
Jan 21,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( v = 20, \, \text{m/s} \)
Solution
To find the velocity \( v \) when the kinetic energy \( E \) is 160,000 J for a vehicle with a mass of 800 kg, follow these steps:
1. **Start with the kinetic energy formula:**
\[
E = \frac{1}{2} m v^2
\]
2. **Plug in the known values:**
\[
160,000 = \frac{1}{2} \times 800 \times v^2
\]
3. **Simplify the equation:**
\[
160,000 = 400 v^2
\]
4. **Solve for \( v^2 \):**
\[
v^2 = \frac{160,000}{400} = 400
\]
5. **Take the square root of both sides to find \( v \):**
\[
v = \sqrt{400} = 20 \, \text{m/s}
\]
**Final Answer:**
\[
v = 20, \, \text{m/s}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To find the velocity when the kinetic energy is 160,000 J, we can rearrange the equation \( E = \frac{1}{2} m v^2 \) to solve for \( v \). First, we have: \[ 160000 = \frac{1}{2} \times 800 \times v^2 \] Now, multiplying both sides by 2: \[ 320000 = 800 v^2 \] Next, divide both sides by 800: \[ v^2 = 400 \] Finally, take the square root of both sides to find \( v \): \[ v = \sqrt{400} = 20 \, m/s \] So, \( v = 20 \, m/s \).
