DISCOVER

# How to Calculate Deceleration Force

Updated March 23, 2017

Suppose that you apply a constant braking force to your car, and it decelerates from a higher velocity to a lower one in a certain amount of time. Then you can use a simple equation from calculus-based physics to solve for rate of deceleration, and therefore for the force that you applied.

Denote the time span of the deceleration (e.g., the pressing of the brake pedal) with the letter t. Denote the initial velocity v0 and the final velocity vf.

Divide the difference of the velocities by t to get the rate of deceleration.

For example, if you brake with constant force for 5 seconds, reducing the speed from 50 to 40mph, then the acceleration is -10mph / 5 sec = -0.89408 meters per second-squared. Note that v0 is subtracted from vf, so that a reduction in speed leads to a negative result.

Use Newton's second law F=ma to find the force of deceleration. Specifically, multiply the deceleration by the mass being decelerated to get the force of deceleration.

For example, for a 2,000kg car, the above deceleration gives 2000 x (-0.89408) = -1,788 Newtons, or 1,788 Newtons (about 182 Kilogram) of deceleration force. This illustrates how much the force of your foot pressing on the brake pedal is magnified by the vacuum-assist and hydraulics of the power braking system in modern automobiles.

#### Tip

You can quickly convert from units with online unit calculators. For example, the unit conversion in Step 2 was done quickly by entering the search phrase, "convert 2 miles per hour to meters per second" into Google.