# How does velocity impact a car accident?

Asked by

raum (

7728)
September 5th, 2019
from iPhone

Car A is traveling on cruise control at 25mph and hits a pedestrian.

Car B is accelerating and while traveling at 25mph hits a pedestrian.

Does the pedestrian sustain the same level of injury in both situations?

F=ma and intuitively it seems an accelerating car would do more damage. But my physics is pretty rusty.

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## 3 Answers

F = ma expresses the amount of force needed to accelerate a body by *acceleration* a. That is, to increase its velocity by a certain amount.

But in a collision f = mv^2 would apply, that is, force in a collision is proportional to mass and to the velocity **squared**. Five times the velocity means 25 times the force. That’s part of why an asteroid striking the earth from some other solar orbit, can be an extinction-level event.

And why getting hit by a car going 10 mph isn’t going to do all that much, but getting hit at 100 mph is going to be major mayhem.

Now, in your example, the force due to velocity would be the same, and would be added to by the force causing the acceleration. So f = mv^2 + ma.

In practice, the force due to acceleration in that case is not going to be a whole lot compared to the 25 mph velocity. Also you didn’t say how much acceleration there was. But imagine the force of standing next to an unmoving car and having it accelerate into you, except most cars don’t usually accelerate particularly fast when already going 25 mph. But it would add that force.

And, what’s relevant to *injury* is also about exceeding thresholds that cause things to get crushed and ripped apart, and about other mechanics of the situation, so every increase in force is a problem. Also the force of acceleration would apply as long as the bodies remained in contact.

That is a most excellent answer. Thanks, @Zaku.

Bodies in motion tend to want to stay in motion. When a car stops suddenly, various parts within continue on, if possible.

Yes, both pedestrians may suffer the same level of injury since the car was travelling at the same speed at impact.

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