Table of contents:

What is acceleration?

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.

Table of contents:

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.

Velocity and Acceleration

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.

Velocity 0 1 2 3 4 5 6 7 8 9m 10 11 12 13 14 15 16 17 18 19 20 21 velocity (hover to zoom)
Acceleration of the red car 0 1 m 3 m 6 m 10 m 15 m 21 m acceleration (hover to zoom) 1st 2nd 3rd sec 4rth sec 5th second 6th 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
TimeTravelled distanceVelocityTotal distance travelled
During 1st sec1 m.1 m/sec.1 m.
During 2nd sec2 m.2 m/sec.1 + 2 = 3 m.
During 3rd sec3 m.3 m/sec.3 + 3 = 6 m.
During 4rth sec4 m.4 m/sec.6 + 4 = 10 m.
During 5th sec5 m.5 m/sec.10 + 5 = 15 m.
During 6th sec6 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.

Objects with different types of motions

Objects in different motions acceleration deceleration acceleration + deceleration velocity, no 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.

Uniform and non-uniform acceleration

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?

Average acceleration :

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 v0 or vi , and a final velocity, say vf  at the end of motion. We simply divide the change in velocity by time to get average acceleration. Average acceleration is equal to  :

change in velocity
change in time
vf - v0
Δ t
Δ v
Δ t

Instantaneous acceleration :

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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