# How is force exerted by an object in collision calculated?

If a car crashes into a wall, what data would you need to calculate the force the car exerted on the wall upon impact?

Currently I’m thinking that you would need the cars mass and velocity(initial) to find the rate of change of momentum, but I remember being taught that rate of change of momentum is f=ma, where f is only the resultant force acting on the object (in this case the car) which isn’t what u want to know.

## 1 Answer

You could easily determine the average force if you knew how long the collision took in time and the initial momentum:

$$F=\frac{\text d p}{\text dt}$$ or $$\frac{\Delta p}{\Delta t}=\frac1{\Delta t}\int F\ \text dt=F_{avg}$$

• Sorry I should I have stated I’m super new to maths and physics, does F=dp/dt mean change in momentum/time? – Ubaid Hassan Apr 12 at 10:17
• @UbaidHassan Yes it's the rate of change of momentum. I know you're "new to math" which is why I also supplied the simpler result of $F_{avg}=\Delta p/\Delta t$. The calculus you might not understand is just the derivation of this for readers who can understand it. – Aaron Stevens Apr 12 at 10:50
• One more question; isn’t there an other way of calculating the force the car would exert on the wall using kinetic energy/distance= force? But I’m not sure what distance would be used – Ubaid Hassan Apr 12 at 10:54
• @UbaidHassan That is trickier because energy will also go into deforming the car, and there isn't a well defined position of the car during the collision. – Aaron Stevens Apr 12 at 12:11