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# Deceleration Formula

Deceleration has actually referred to the acceleration in a reverse way. We know that acceleration means the rate at which an object speeds up, that means deceleration means the rate at which an object slows down. For example, when we are using brake during driving, we are taking benefits of deceleration to reduce the speed of the vehicle. In this article, a student will learn about deceleration, its meaning and also deceleration formula with examples. Let us learn the concept!

Source:en.wikipedia.org

## Deceleration Formula

### Concept of Deceleration

Anytime we are in a vehicle and we feel moving forward relative to the vehicle, then we are decelerating. Here, deceleration is a special case of acceleration whereby it only applies to objects slowing down. Therefore, it is the rate at which an object slows down.

Acceleration is a vector because it has to be reported as a magnitude with a direction. In cases of one-dimensional motion, negative and positive signs are used to indicate the direction. Thus, if the signs are negative then the object is decelerating.

Deceleration is the opposite of acceleration. The deceleration will be computed by dividing the final velocity minus the initial velocity, by the amount of time is taken for this drop in velocity. The formula for acceleration can be used here, with a negative sign, to identify the deceleration value.

### The Formula for Deceleration

It is computed as:

Deceleration = $$\frac {Final \; Velocity – Initial \; Velocity}{Time\; taken}$$

It is denoted by –a, where a is acceleration.

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 or $$ms^{-2}.$$

## Solved Examples on Deceleration Formula

Q.1: A vehicle is moving with a uniform velocity of 54 kmph. It is brought to the rest position after traveling a distance of 5 m. Calculate the deceleration produced by brakes?

Solution:

As given here,

Initial velocity, u = 54 Kmph,

Final velocity, v = 0,

Distance covered, s = 5 m

Thus we can apply second formula,

a = $$\frac {v^2 – u^2} {2s}$$

a = $$\frac {0^2 – 54^2} {2 \times 5}$$

So,

a = – 291.6 $$ms^{-2}$$

Therefore value of deceleration will be – 291.6 $$ms^{-2}.$$

Q.2: You and a friend are driving on the highway road at 150 km/hr. When you see a police van ahead, you decelerate to 120 km/hr, which takes the time 2 seconds. What was the deceleration in km/sec² ?

Solution:

As given here,

The initial velocity, u = 150 kmph

i.e. u = $$150 \times \frac{1}{3600} hr per sec$$

u = 0.042 km per sec.

The final velocity, v = 120 kmph

i.e. v = 120 $$\times \frac{1}{3600} hr per sec$$

v = 0.033 km per sec.

The time, t = 2 sec.

Now ,

a = $$\frac{v-u}{t}$$

a = $$\frac{0.033-0.042}{2}$$

So,

a = – 0.0045 km $$sec^{-2}$$

Therefore value of deceleration will be- 0.0045 km $$sec^{-2}.$$

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