We see objects moving around. These objects do not always move at a constant speed, or in a constant direction. For example, planets revolving around the sun change their direction at every point, cars moving on a road subjected to traffic have different speeds at different point of time. How do we quantize this change in their velocity, both the magnitude and direction? Here, we introduce the term acceleration, which is the rate of change of velocity of an object. But how does it work in terms of change in direction of velocity?

## What is Acceleration?

Whenever we are getting late for school and your father is driving you to school, you ask your father to hurry up and in response to that, you feel the car going faster. This is called acceleration. So what is acceleration?

From the above observation, it can be said as the vehicle’s capacity to gain speed. It is actually a change in velocity. Mathematically, acceleration is defined as a rate of change of velocity.

The acceleration formula is given as:

Acceleration (a) = \( \frac {change~in~velocity}{Time~Taken}\)

\(~~~~~~~~~~~~~~~~~~~~\)

So unit for acceleration is m/s^{2}. It can also be interpreted using Newton’s second law i.e.

*F* = *ma*

Hence a body is accelerated only if a net external force acts on the body. And the acceleration produced is inversely proportional to mass. Based on the direction of velocity it can be positive or negative. When both velocity and the external forceact in the same direction then the acceleration is positive or the velocity of the body increases. For example, when the accelerator pedal of the vehicle is pressed, the velocity increases. Similarly, when they act in opposite directions the acceleration is said to be negative or the velocity decreases. An example is, braking pedal of a vehicle when we press it the velocity decreases. There is another classification of acceleration that is uniform and non – uniform. If the acceleration remains constant for a given interval of time it is said to be uniform while if it changes it is said to be non – uniform. When it is uniform, we can use equations of motion. We should keep in mind that these equations can’t be used when a body is accelerated non-uniformity. Graphically they can be represented as follows.

### Uniform and Non-uniform acceleration

So can we have a situation when speed remains constant but the body is accelerated? Actually, it is possible in circular where speed remains constant but since the direction is changing hence the velocity changes and the body is said to be accelerated.

### Average acceleration

The average acceleration over a period of time is defined as the total change in velocity in the given interval divided by the total time taken for the change. For a given interval of time, it is denoted as *ā*.

Mathematically,

Where *v _{2}* and

*v*are the instantaneous velocities at time

_{1}*t*and

_{2}*t*and

_{1}*ā*is the average acceleration.

## Velocity-time graph

**Average acceleration:** In the velocity-time graph shown above, the slope of the line between the time interval *t _{1}* and

*t*gives the average value for the rate of change of velocity for the object during the time

_{2}*t*and

_{1}*t*.

_{2}**Instantaneous acceleration: **In a velocity-time curve, the instantaneous acceleration is given by the slope of the tangent on the v-t curve at any instant.

### Positive, negative and zero acceleration

Consider the velocity-time graph shown above. Here, between the time intervals of 0-2 seconds, the velocity of the particle is increasing with respect to time; hence the body is experiencing a positive acceleration as the slope of the v-t curve in this time interval is positive.

Between the time intervals of 2-3 seconds, the velocity of the object is constant with respect to time; hence the body is experiencing zero acceleration as the slope of the v-t curve in this time interval is 0.

Now, between the time intervals of 3-5 seconds, the velocity of the body is decreasing with respect to time; hence the body experiences a negative value of the rate of change of velocity as the slope of the v-t curve in this time interval is negative.

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