Transforming kinetic energy into thermal energy

[nlingraham]

Homework Statement

Two cars collide head on while each is traveling at 80 km/h. Suppose all their kinetic energy is transformed into the thermal energy of the wrecks. What is the temperature increase of each car? You can assume that each car's specific heat is that of iron.

Homework Equations

K=1/2mv²

Q=mcΔT

1/2mv²=mcΔT

∴ ΔT=v²/2c

The Attempt at a Solution

I worked it out using 80 km/h for v and 449 J/kg * K for c and got 7.13 K. My question is if this is right, and if it is can someone explain to me how the units cancel out to give just K?

 

[voko]

Express J in terms of kg, m and s. What is the dimension of c then?

 

[nlingraham]

Ok, I got it. J=kg*m²/s². So that meant I had to convert 80 km/h to 22.22 m/s for everything to cancel out. I ended up getting .55 C. Thank you for your help.