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# Change in Velocity

In this article, we will discuss what a change in velocity is and its formula along with some examples and related questions and answers.

It is important to note here that change in velocity can happen both w.r.t time and position.

• when velocity changes w.r.t. the time it is called acceleration.
• when it is measured w.r.t. position then it is called velocity gradient.

## What is change in velocity?

We all know that velocity is the rate of change of position of a moving object with respect to time.

Change in velocity, also known as acceleration, is the rate at which an object’s velocity changes over time. It can be calculated by taking the difference in velocity over a specific period of time and is typically measured in meters per second squared $(m/s^2)$.

A positive acceleration indicates that an object is speeding up. In contrast, a negative acceleration indicates that an object is slowing down or moving in the opposite direction.

### Change in velocity formula

The formula for change in velocity is:

$$Acceleration = \frac{(\text{final velocity} – \text{initial velocity})}{time}$$

or,

$$a = \frac{(v_f – v_i)}{t}$$

Where:
$a =$ acceleration
$v_f =$ final velocity
$v_i =$ initial velocity
$t =$ time

It can also be represented as the derivative of velocity with respect to time, which is also known as the second derivative of position with respect to time.

### Symbol

It is represented by the symbol $\Delta v$ where, $\Delta$ is a greek uppercase letter usually used to represent the change in some quantity in physics, chemistry or mathematics.

### Examples

1. A car accelerating from a stop sign to a set speed on a highway. The car’s velocity is increasing, so it is experiencing a positive acceleration.
2. A rollercoaster starting to go down a hill. The rollercoaster’s velocity is increasing, so it is experiencing a positive acceleration.
3. A ball is thrown into the air and then falls back to the ground where the velocity of the ball changes continuously.
1. As the ball is thrown upwards, its velocity starts decreasing up to the max height.
2. When the ball reaches its highest point, its velocity becomes zero.
3. As the ball falls back to earth, its velocity increases due to gravity and just before the ball hits the ground its speed is maximum at that point
4. A car braking to a stop at a red light. The car’s velocity is decreasing, so it is experiencing a negative acceleration (also known as deceleration)

1. How does this change in velocity happen?
Velocity is a vector quantity that has magnitude as well as direction. Change of velocity takes place when one or both of them change.
2. What are the dimensions of the change in velocity?
Its dimension is the same as the dimension of acceleration because the change in velocity with respect to time is defined as acceleration.
So, the dimensions are
$[LT^{-2}]$