Let’s see the difference between acceleration ad deceleration.

**Acceleration is a rate of change of velocity within a required time along a positive or negative direction, but what is deceleration? Whenever an object slows down during its motion, it decelerates. So we can say that in acceleration and deceleration, velocity is changing with respect to time, but What is the difference between Acceleration Vs Deceleration?**

**Acceleration Vs Deceleration**

Acceleration | Deceleration |

The rate of change of velocity vector of an object in the direction of force is called acceleration | The acceleration that slows down the motion is called deceleration. It is always opposite to the direction of motion. |

It is a vector quantity and has magnitude as well as direction. | Deceleration is also a vector quantity. |

Acceleration can be positive and negative. | Deceleration can also positive or negative. |

Whenever an object speeds up, it accelerates. | An object always decelerates when it slows down. |

A moving car accelerates when it increases its velocity. | The car starts to decelerate when breaks applied to it |

**Acceleration: Detailed analysis**

**Acceleration is a vector quantity. When the body changes its velocity by changing magnitude (Speed) or direction, it accelerates**. SI unit of acceleration is m/s^{2}. Acceleration is always in the order of applied force on a body. It can be positive or negative. Whether the acceleration of a body is positive or negative is depends upon the following two factors,

- the coordinate system used to describe the motion
- weather the body speeding up or slowing down

To learn more about negative acceleration, see the post on negative acceleration

**Vector form of acceleration**

We know that acceleration is a rate of change of velocity to time,

If we resolve the velocity vector, i.e.

Where

[latex]v_{x},v_{y},v_{z}, are component of velocity along x, y, z respectively [/latex] and i, j, k are the unit vector in the x, y, z-axis, respectively.

Then,

We can find out the average acceleration or an instantaneous acceleration of a moving body. Now, what is average acceleration? And what is fast acceleration?

## **Average acceleration**

Consider a car moving with a continuously changing velocity. Its average acceleration is the ratio of a total speed change during a motion to the required time to complete that motion. Mathematically it is represented as,

where a_{ave} – Averege acceleration

v_{f} – final velocity

v_{i} – initial velocity

**Instantaneous acceleration**

Instantaneous acceleration is acceleration in a particular time instant during motion. Mathematically it is denoted as,

**Deceleration**

**A moving object slows down by losing its speed, and the rate by which it loses its velocity is called deceleration. Deceleration is always in the opposite direction of the velocity of the moving object**. The SI unit of deceleration is m/s^{2}. The following formulae give the magnitude of deceleration,

Therefore,

v- final velocity

u- initial velocity

t- time of motion

Here, the negative sign indicates that deceleration is opposite to the direction of acceleration.

**Sign of Acceleration & Deceleration**

As we discussed earlier, a sign of acceleration depends upon two factors, namely, the coordinate system chosen to describe the motion and whether the object is speeding up or slowing down. Deceleration is also dependent upon these two factors.

To understand this correctly, consider the motion of a car in one dimension. We can divide the motion of a car into four cases; these are as follows,

**Case1**-A car is moving in a forward direction and speeding up

**As the vehicle is speeding up in a forward direction, deceleration is zero, and acceleration is in the direction of velocity. Both velocity and acceleration are positive in this condition.**

**Case2**– A car is moving in positive x-direction and slowing down.

As we know, deceleration is always associated with the slowing down of motion. In this case, the car is slowing down while moving in + x-direction. The friction force is responsible for the slowing down of the car and is in – x-direction; therefore, the acceleration of a car is also in – x-direction**. As the car is slowing down, it means a car is decelerating in the negative x-direction. Therefore, in this case, we can say that negative acceleration and deceleration are the same.**

**Case3**– A car is moving in a negative X- direction and slowing down.

In this case, the car is decelerating, and its direction is along the positive x-axis. Hence the deceleration of the car is positive; this proves that slowdown can be positive.

**Case4**– A car is moving in negative x-direction and speeding up

In this case, the vehicle is speeding up in –ve x-direction, so it has no deceleration. As the direction of motion is negative, so the acceleration of the car is also negative.

Hence deceleration and negative acceleration are not necessarily equal.

**Solved examples of acceleration and deceleration**

**A man starts to walk on a road with a velocity of 0.5 m/s. After 4 minutes, its velocity is 2 m/s. What is the acceleration of that man during motion?**

Solution-

Given, initial velocity, u = 0.5 m/s

Final velocity, v = 2 m/s

Time, t = 4 minutes = 4×60 = 240 sec

To find: acceleration of a man

By using the formulae for average acceleration,

0.00625 m/s^{2} is the acceleration of a man within the motion.

**A car moves with a uniform velocity of 40 km/hr from point A and stops at point B. A car completes its motion from point A to B within 5 hours. What will be the deceleration of the car in km/hr**^{2}?

^{2}?

Solution,

Given the initial velocity of the car, u = 40 km/hr

Final velocity of car, v = 0 km/h

Time to complete the motion, t = 5 hr

To find: deceleration of a car

By using the formulae of deceleration

Here, the negative sign indicates the direction of deceleration

**= – 8 km/hr ^{2}**

-8 km/ hr^{2} is the deceleration of the car within motion.