\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}

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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:**
$$
v = 20, \, \text{m/s}
$$
$$ v = 20, \, \text{m/s} $$

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