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. \( v= \)

To find the velocity when the kinetic energy \( E \) is 10,000 J for a vehicle with a mass of 800 kg, we start with the kinetic energy formula: \[ E = \frac{1}{2} m v^{2} \] Plugging in the values: \[ 10,000 = \frac{1}{2} \cdot 800 \cdot v^{2} \] This simplifies to: \[ 10,000 = 400 v^{2} \] Dividing both sides by 400: \[ 25 = v^{2} \] Taking the square root of both sides gives us: \[ v = 5 \, \text{m/s} \] For graphing the equation \( E = \frac{1}{2} \cdot 800 \cdot v^{2} \), you will produce a parabolic curve starting at the origin (0,0) and opening upwards, representing the increasing kinetic energy as the velocity increases. Thus, the final answer is: \( v = 5 \) m/s