In its simplest term, acceleration is the rate
of change of velocity of a moving object w.r.t. time.
When velocity changes, acceleration occurs.

- ● What is acceleration
- ● Velocity and acceleration
- ● Uniform and non-uniform acceleration
- ● Average acceleration
- ● Instantenous acceleration

Before understanding the term acceleration, please have a look in the pages
displacement
and velocity .

Let an object move with a velocity of 9 meter/sec.,
which does not change throughout a certain period of time.
This is defined as **constant velocity.**

In such case, there is **no acceleration**.
At any point of the travel-path, the velocity will be exactly 9 meter/sec.

If the said object changes its velocity due to some reason,
say, from 9 meter/sec. to
12 meter/sec. after a certain
period of time, then the object is said to have gained **acceleration**.

Even if the object changes its direction without changing the current speed,
still it gains acceleration.
Simply, acceleration is defined by the fact how fast the velocity is changing.

Click the following three buttons to animate the toy-cars.
In case of the green car, there is a constant velocity.
It travels at the rate of 3 meter per second, or
**21m** in **7** seconds; this velocity is expressed
as 3 m/sec,
and read as 3 meter per second.

There is no change in velocity throughout the path.
At any instant of the path, velocity is exactly 3 m/sec.
So there is no acceleration, or acceleration = 0.

But in case of the red car, it starts with an initial velocity of zero
(it starts from rest) when time=0, or t=0.

Then in the 1st second it travels 1 meter, so velocity is 1 m/sec.
But in the 2nd second, it travels another 2 meter,
so velocity at 2nd second is 2 m/sec.
In the 3rd second the car travels another
3 meter (velocity now is 3 m/sec), and so on.
At the 6th. second,
the car has a velocity of 6 m/sec.

Different velocity at different time | |||
---|---|---|---|

Time | Travelled distance | Velocity | Total distance travelled |

During 1st sec | 1 m. | 1 m/sec. | 1 m. |

During 2nd sec | 2 m. | 2 m/sec. | 1 + 2 = 3 m. |

During 3rd sec | 3 m. | 3 m/sec. | 3 + 3 = 6 m. |

During 4rth sec | 4 m. | 4 m/sec. | 6 + 4 = 10 m. |

During 5th sec | 5 m. | 5 m/sec. | 10 + 5 = 15 m. |

During 6th sec | 6 m. | 6 m/sec. | 15 + 6 = 21 m. |

The velocity changes by
1 meter per second in every second,
which implies that the acceleration here is
1 meter per second per second.
This is the unit of acceleration, which can be written as
1 m/sec/sec or
1 m/sec² or
1 m.sec⁻² .

**Units of acceleration :** The SI unit of acceleration is
meter/second/second or
m/sec² or
m.sec⁻².
It may actually be expressed in the format length/time/time.

There is one important formula with the variables :
intial velocity, final velocity, acceleration and time.
This is known as

v = u + at

where u = intial velocity,
v = final velocity,
a = acceleration, and
t = time.

In case of the red car, we have,

intial velocity u = 0,

final velocity v = 6 m/sec.

time t = 6 sec.

We know,

v = u + at

⇒ 6 = 0 + a × 6

⇒ 6a = 6

⇒ a = 1

so, acceleration a = 1 m.sec⁻²

When velocity reduces by time we call this **deceleration** or **retardation**.
This is also known as **negative acceleration**.

In the first path, the velocity is continuously increasing
and this resulted an **acceleration** of the object.

In the second path, velocity of the object is decreasing
as visible in the animation.
As a result, **deceleration** or **retardation** has occured,
which is also known as **negative acceleration**.

In the third path, velocity of the car is increasing
in the first half of the path,
then it is decreasing for rest of the path. So,
**acceleration** and **deceleration** both have occured.

In the fourth path, velocity is constant throughout the path,
hence, no acceleration or deceleration happened here.

When direction of an object changes, speed remaining constant,
velocity changes. This is because velocity always considers
both **speed** and **direction**.

And when velocity changes, acceleration occurs.
So, an object moving through a circular path
will have acceleration even if the speed is constant.

When an object travels in a straight-line so that
its velocity increases or decreases
by equal amounts in equal intervals of time,
then the acceleration is called uniform acceleration.

Example : When an apple falls from the tree on the
ground, it obtains a uniform acceleration of 9.8 m.sec⁻².
This is the **acceleration due to gravity**
of our earth.

On the other hand, a body is said to have non-uniform acceleration
if its velocity increases or decreases
by **unequal amounts in equal intervals of time**.

Example : If you are going home by your school-bus,
the bus will obtain non-uniform acceleration throughout the path, because
of frequent use of the brakes and throttle in the traffic.

Can you say which of the four motions has non-uniform acceleration
in the above animation?

When we calculate acceleration over a finite
period of time, then it is known as average acceleration.
The object will have an initial velocity at the beginning of motion, say
v_{0} or v_{i} ,
and a final velocity, say v_{f} at the end of motion.
We simply divide the change in velocity by time to get average acceleration.
Average acceleration is equal to :

a

=

change in velocity

change in time

change in time

=

v_{f} - v_{0}

Δ t

Δ t

=

Δ v

Δ t

Δ t

For measuring instantaneous acceleration we take a very small
interval of time, a very small time-period. What is the acceleration
during that small period of time?
That is the instantaneous acceleration.
But the interval of time should be so small that it is almost zero.

To simplify, the acceleration of an object at any instant is known as
instantaneous acceleration.

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