I have the question:
"Calculate the kinetic energy, $E_k$, when a car of mass $1500$ kg travels at a speed of $108$ km/h."
I converted the $108$ km/h to $108000$ m/h by multiplying by $1000$. I then divided $108000$ by $60$ to get minutes and then again by $60$ to get $30$ m/s I then put these values into the equation for kinetic energy and got $675000$ Joules.
So the final answer I get for this is $675000$ Joules [J] is this correct and if not could you please explain where I went wrong ?
On
Kinetic energy is simply ${\frac{mv^2}{2}}$, where $v$ is velocity and $m$ is mass. Since the velocity given to you is in $Km/hr$ and the standard unit of velocity is $metres/sec$ so on converting the velocity to $m/s$ you get $v=\frac{108\times5}{18}=30 m/s$.
The mass given to you is $1500 kg$ so the Kinetic energy becomes ${\frac{mv^2}{2}}=\frac{1500\times 30\times30}{2}= 675000$ Joules.
Your conversion from km/h to m/s is correct and as long as you used $p^2/2m$ where p is the momentum and m is the mass or $1/2mv^2 $ the more familiar one you are ok.