Braking a car and running it into a tree both exert the same amount of force to stop the car, but the latter is more painful for the driver because it occurs over a shorter amount of time. This phenomenon is due to the impulse of force. You can calculate the impulse of force by multiplying force times the amount of time the collision takes or by multiplying the mass of the object by the change in velocity during the collision. Combining these equations enables you to solve for the average force during the collision.
Subtract the velocity of the moving object after the collision from its velocity before the collision. For example, If a car travelling at 20 feet per second (ft/s) hits a guardrail and comes to a complete stop, the difference in velocity is 20ft/s - 0ft/s = 20ft/s. Note that if the object moves in the opposite direction after the collision, you indicate this by attaching a negative sign to the velocity. So if the car bounced off the crash barrier and moved at 2ft/s in the opposite direction, the change in velocity would be 20ft/s - (-2 f/ts) = 22ft/s.
Multiply the change in velocity by the mass of the moving object. If you are using English units, divide its weight in pounds by 32 to convert to slugs. If the car weighs 907 Kilogram, for example, divide by 32 to get 62.5 slugs. Multiply 62.5 slugs by 20ft/s to get 1,250 slugs*ft/s.
Divide the result by the time of the collision. If the collision between the car and the crash barrier took 1 second, for example, divide 1,250 slugs_ft/s by 1 second to get 1,250 slugs_ft/s^2. One slug*ft/s^2 equals one pound, so the average force of the collision was 567 Kilogram.
- If both objects in the collision were moving originally, calculate the average force of each object and add them together to get the total average force of the collision. Convert all quantities to appropriate units before beginning the calculation. Use kilograms, meters and seconds for metric units or slugs, feet and seconds for English units.