On braking, 250kj of heat was produced when a vehicle of total mass 100kg was brought to rest on a level road. what is the speed of the vehicle just before the brakes were applied?

The speed of the vehicle would be sqrt 250 000 J / 0.5 * 100 kg =~70.71m/s. However this only is the speed when ALL energy is converted into heat, and that is absurd. The temperature of the vehicle (which I suggest is mostly made out of steel) should rise with 250 kJ / 100 kg * 0.49 kJ/kgK = 5.1 K, which is quite a lot for just braking. So how much should the speed be for normal energy conversion from the total amount of energy? We don't know the speed the vehicle slows down, and even if we knew it would be hard to calculate. So it is quite unrealistic, but the number you are looking for is approximatly 70.71 m/s.

That would be the corect answer hope this