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 10000 J? Write all answers on the same line separated by commas. $$ v= $$

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UpStudy AI · Accepted Answer

To find the velocity $$ v $$ when the kinetic energy $$ E $$ is 10,000 J for a vehicle with a mass of 800 kg, follow these steps:

1. **Kinetic Energy Formula:**
   $$
   E = \frac{1}{2} m v^2
   $$
   
2. **Plug in the Known Values:**
   $$
   10,000 = \frac{1}{2} \times 800 \times v^2
   $$
   
3. **Simplify the Equation:**
   $$
   10,000 = 400 v^2
   $$
   
4. **Solve for $$ v^2 $$:**
   $$
   v^2 = \frac{10,000}{400} = 25
   $$
   
5. **Take the Square Root:**
   $$
   v = \sqrt{25} = 5 \, \text{m/s}
   $$
   
**Answer:**
$$ v = 5 \, \text{m/s} $$
$$ v = 5 \, \text{m/s} $$

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