# Deceleration Formula

Deceleration Formula – You’ve probably observed that when we’re stuck in traffic, we tend to slow down our bikes. Deceleration is described as a reduction in speed as the body moves away from the starting position. Deceleration refers to backward acceleration. We know that acceleration is the rate at which an object accelerates, and deceleration is the rate at which an object slows. For example, when we use the brake while driving, we take use of deceleration to lessen the vehicle’s speed. In this article, students will learn about deceleration, its definition, and the deceleration formula with examples. Let us learn the concept!

## Deceleration Formula

The Deceleration Formula is a pretty regular occurrence in our everyday lives. When driving, people may notice that when they feel like they are moving forward relative to the car, they are actually experiencing deceleration (a slowing of our velocity). The Deceleration Formula is a specific case of Acceleration in this context, as it only applies to things slowing down. In a nutshell, it is the pace at which an item slows.

Acceleration is a Vector property of a moving object. This is due to two factors: magnitude and direction. In the case of one-dimensional motion, negative and positive signs are employed to indicate direction. If the signals are negative, the thing is said to be decelerating or retarding.

Deceleration can be thought of as the inverse of acceleration. The  Deceleration Formula may be computed by dividing the final velocity minus the beginning velocity by the time it took for the velocity to decline. To determine the Deceleration value, apply the Acceleration formula with a negative sign.

The Deceleration Formula, also known as retardation or negative acceleration, is the acceleration that operates in the opposite direction of motion.

The Deceleration Formula is as follows –

 $$Deceleration Formula (a)=\frac {Final \; Velocity – Initial \; Velocity}{Time\; taken}$$

Deceleration also is known as negative acceleration. Hence it is denoted by – a.

If starting velocity, final velocity and time taken are given, then Deceleration Formula is given by,
$$a = \frac{v-u}{t}$$
If we have initial velocity, final velocity, and distance traveled, then we can compute deceleration as:
$$a = \frac {v^2 – u^2} {2s}$$
Where,

 -a Deceleration u Initial velocity v Final velocity s Distance t Time

In order to calculate the deceleration of the body in the motion, we use the Deceleration Formula. It is expressed in meter per Second Square.

### Deceleration Formulas with Solved Examples

Example 1: An object moving with a Velocity of 56m/s is brought to rest in 8 seconds by a constant Deceleration. Find the Deceleration applied.

Solution : Here, initial Velocity(u) = 40m/s

Final Velocity(v) = 0 m/s

Deceleration = a

Time = 8 s

From 1st equation of Motion:

v = u – at

0 = 56 – a.8

a = 56/8

a = 7 m/s².

Example 2 : An automobile moving with a uniform velocity of 63 Kmph is brought to rest in travelling a distance of 7 m. Calculate the deceleration produced by brakes?

Solution:

Given: Initial velocity u = 63 Kmph,

Final velocity v = 0

Distance covered s = 7 m

We know that v2 = u2 + 2as

Deceleration a = v2 u2 / 2s

Deceleration a  = 0 – (63000 )2 / 2(7)

a=-283.5 x 10m/s2

### Deceleration in Gravity Units (G’s)

One of the two methods given here can be used to compute the Deceleration rate when an item is subjected to gravity, if the result is desired in terms of gravity units (G).

The First Method:

Subtract the Deceleration from the usual gravitational acceleration (which is 9.8m/s2). The average amount of G’s delivered to the moving item to achieve the Deceleration Formula is given as the outcome.

Students may comprehend this by using the following example: Determine the G Force necessary to bring the automobile to a halt with a deceleration of -27.66 feet per second squared.

The moving car’s computed deceleration is 27.66 feet per second per second. The deceleration equals: 27.66/32 = 0.86 G’s

### Determining Deceleration Using Speed Difference and Time

This is fairly straightforward. Subtract the finishing speed from the initial speed first.

Convert the speed difference to units of speed compatible with the to-be-calculated acceleration, typically metres per second. If the speed is given in miles per hour, multiply it by 0.278 to get the speed in metres per second.

Then, divide the speed change by the time the change happened. The result of this computation is the average Deceleration rate.

### Determining Deceleration Using Speed Difference and Distance

Convert the beginning and ending speeds to usable units for computing the Acceleration (metres per second). Next, square the starting and ending speeds.

Subtract these squares from the previous step as follows: the square of the final speed minus the square of the beginning speed.

Divide the distance by two. This is the average rate of deceleration.

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