Let's say I want to teach kinetic and potential energy and I'd like to use an example that students can remember. The original idea is to show that speed (being squared) in the kinetic energy formula proves to be very important in the energy being delivered to a body. If a car travels in a 30 km/h limit zone with 34 km/h, how much more impact do those 4 extra km/h make when hitting a pedestrian (no braking)? You can compute the Joules difference but it doesn't say much on how it impacts the pedestrian. I thought about making this kinetic energy equal to the potential energy of a body falling to the ground and using the computed equivalent heights to show how much more dangerous it is. Is this a too simple model to be good enough?
Asking "how much more impact" is not a well defined question so it will be difficult to associate a quantity to it. You could indeed calculate the height corresponding to the PE equal to the extra KE. It does not mean that the effects on the body are the same in the two cases. In this case, considering a 2000 kg car and 100 kg man, the extra KE of the car will correspond to the man falling from about 20 m. But the extra energy is not transferred to the man. The tricky part is to find how much energy is transferred to the man by impact and this is not trivial. The collision is neither perfectly elastic, nor perfectly inelastic (they don't stick together). So the amount of KE transferred will depend on the details of the collision. Maybe you could consider an elastic collision as a model (the energy transferred to the body is maxim in this case) and calculate the difference in energy transferred. If you convert it to PE of the body it will be less than 4 m, still significant and more realistic probably than the 20 m. People often survive accidents produced by cars running at 34 km/h but not so falls from 20 m.
Yes, the example makes sense. Assuming the poor pedestrian was at rest before the impact hence its momentum will be zero too. Therefore the car will transfer its entire Kinetic Energy to the pedestrian and he will start moving at the velocity at which the car was moving earlier(ignoring all the frictional forces). You can absolutely calculate the impact made by car due to a 4 km/h difference by computing the Joule difference. As the example of a body falling to the ground from a certain height, this scenario will not exactly match with the one of the car accident, because in this example of falling body, the Potential Energy will be converted into Kinetic Energy and hence on impact the pedestrian will feel the same force, but because of the presence of ground beneath him he will then have no Kinetic Energy and will remain at rest. The impact caused by both will be same but the final state of motion of the pedestrian will change.