# How to Calculate Deceleration Force

Written by paul dohrman
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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.

Skill level:
Moderate

## Instructions

1. 1

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.

2. 2

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.

3. 3

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.

#### Tips and warnings

• 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.

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