A friend of mine knocked someone down a few years ago and I was discussing the conversation with a colleague that I had with the guy at the time of the accident.

The driver said to me “When I hit the guy (who stepped out in front of him without looking) I was only doing about 25mph but I was accelerating? Does that make the impact worse?”

No I know bugger all about physics but common sense told me that it would be something to do with terminal velocity – so if he was doing 25mph it wouldn’t matter what speed he was doing before that.

The colleague I’ve just had the discussion with isn’t so sure though.

So whats the answer then? If he was traveling at a constant 25mph or had accelerated to 25mph is there a difference in force?

My common sense says know but I realise science doesn’t worl like that.

Biggest difference I guess would be on how the attitude of the car affected where and how he was hit and thrown afterwards. The bonnet would have been higher under acceleration, lower under braking.

Edit: and how long it took him to move his foot to the brake, and what affect the delay in braking made to where the car was in relation to the person who was hit and what happened to him afterwards.

Energy of impact would be half mass of car times speed squared.
If accelerating the duration of the impact could see the speed increase by a little so you could average out the initial and final impact speeds.

He didn’t brake as the guy just stepped into his path, but possibly stopped accelerating, so at the time of impact he was accelerating but was obviously at x speed at the instant the ped was hit.

and it was a glancing blow rather than a centre of the car impact so actual impact time would be negligible.

Worse, IMO – not because of physics, but cod psychology:

presumably “25” is an estimate, assuming he hadn’t just looked up from the speedo to see what that bump was ?

My money’s on 30+, wishful thinking, poor extrapolation and subconsciously alleviating any feelings of guilt

My money’s on 30+, wishful thinking, poor extrapolation and subconsciously alleviating any feelings of guilt

That’s not the point of the question. If it makes you feel better replace ’25’ with ‘x’, the actual figure is irrelevant.

GCSE physics tells me the kinetic energythe car had when it hit the poor chap, and which his body had to absorb was 1/2(m *v squared) where v stands for velocity not acceleration.

Whether it was an elastic or an inelastic collision is a different matter.

The squared bit of the v is important as it means even small increases of speed means large increases of energy that human bodies have to absorb when they are hit.

So its terminal velocity at time of impact then and whether he was accelerating or not makes no difference?

Not to how hard the guy was hit.

But there would have been other things going on besides the actual speed at impact. The bonnet would have been a few (4? 6? more?) inches higher under hard acceleration compared to hard braking, and that would mean the guy suffered those initial impact injuries in different places as a result. Broken femur rather than mangled knee, for example.

The point of impact might have made the difference between being scooped into the air or going underneath the car. It would have taken longer for the car to stop if the driver wasn’t already braking, so if poor chap was underneath the car, he’d have been dragged for longer; if he was up the air, he might have landed on the car or on the road, depending on how fast the car stopped afterwards.

Edit: you said it was a glancing blow, so not all of that is relevant.

Wild guess that Ned is right, how and where the poor chap was hit due to the attitude of the car is probably more important than any slight increase in speed during the collision (but as gwaelod said speed at time of start of collision is very important)

ie if you were hit at X speed whether the driver was braking from a higher speed or accelerating from a lower speed probably doesn’t matter, you still got hit with Y energy. Your survivability is probably more dependant on which causes less injury, low down bumper with car pitched toward you or higher bumper with car pitched slightly back (don’t know the answer to that – probably varies from vehicle to vehicle)

Interesting question that, does the power provided by the engine add to the force of impact? My Thursday afternoon brain thinks it may.

What about if it happened on a conveyor belt?

Yes his velocity (speed) not his acceleration is probably most important, but as others have pointed out the angle of the car may be important as it may have affected how that energy was applied to the chap….causing local organ failure. At this point we should probably also consider whether it was an elastic or inelastic collision but either way the speed at impact is a factor not the acceleration I think, but am prepared to be corrected on that as both initial and post collision speeds are used….and I am aware this is more complex than tennis balls in a physics lab

PedantOn ‘Terminal’ velocity is irrelevant by the way unless the car was falling from great height. PedantOff

No broken bones and the numpty ped walked away uninjured.

Possibly speed being applied after impact is factor..see inelastic collision equation

Looking at it this way…

replace ’25’ with ‘x’, the actual figure is irrelevant

Now if x=0 it’s gonna hurt more if the car is accelerating than if at a constant speed, or braking.

As mark90 mentions, the speed of the car and the level of acceleration both have an effect on the length of the ‘incident’. If your stood in fornt of a stationary car, whcih accelerates from standstill into you then by the time your head hits the car it will be going faster than when it hit your legs, at 20mph the difference in speed over the time of the event is minimal, even more so at higher speeds.

Also, the mass of the car plays a part. Hitting the person would slow the car down, so if it was accelerating then an increase in transmitted force would happen but as the mass of the car is far greater than the person it would again be small.

Terminal velocity applies to a falling object where gravity balances drag, so not the right term in this case.

I reckon two things apply – energy and inertia

Ass stated, energy of a car depends on velocity, so if the car is doing 25 at the very point of impact, the energy it has (and can impart) is the same at that one instant, no matter if accelerating, constant or decelerating.

Inertia says the struck person will need to be accelerated from 0 to 25mph (or slightly less, as the car will also have the force of the person acting on it, trying to slow it down). In this case, the acceleration of the car would then take effect and decide what happens in the moments following the impact. Energy is still being added for the duration of the impact. So I’d rather be struck at 25mph by a braking car than an accelerating one (if I had to be struck at all – not offering to try it!)

I think that’s about right…