**Average speed and average velocity**

The average speed is defined as the ratio of the total
distance traveled by the body in the total given time. The average velocity is
defined as the ratio of the total displacement covered by a body in the total
time.

Speed is a scalar quantity which has only a magnitude but not
specified direction. Velocity is a vector quantity which has both magnitude and
direction and also satisfies the laws of the vectors.

In any given situation we can calculate the average speed and
average velocity. If a body comes back to its original position after a certain
time, its average velocity can become zero but it will have its average speed.

When we are talking about a straight-line motion where the
body is going to have only a forward motion, there won’t be any significant
difference in terms of the magnitude of average speed and average velocity. In
a given situation we have to calculate average speed or average velocity.

**Problem and solution**

A body moves half of the time with one velocity and during
the other half of the time it moves with a different velocity. Find the average
of those velocities?

Basing on the definition of average velocity, we can write it
as the ratio of total displacement to the total given time. Let in the first
half of the time it covers a specific distance and the remaining half of the
time it is covering some another distance. The total distance is the sum of
these two distances. The total time ease some of the two halves of the time
which is equal to the total time of the journey itself. As distance is not
given in the problem, we have to express it in terms of velocity and time. We
know that the distance is defined as the product of velocity and time and
taking that into consideration, we can derive the equation for the average
velocity of the above case as shown below.

**Problem and solution**

If a body covers half of the displacement with one velocity
and the second half of the displacement with some another velocity, find its
average velocity?

We can solve this problem also basing on the same formula as
the average velocity is the ratio of total displacement to the total time. But
solving this problem is slightly different because if the distance is given and
time is not given.

Here we have to convert the time in terms of displacement and
velocity and the problem is solved as shown below.

Thus the average velocity into different situations could be
different.

**Problem and solution**

A body is covering three equal parts of the total
displacement with three different velocities. Find its average velocity?

This problem is also solved under the same lines, basing on
the very definition of the average velocity is the total displacement per unit
time. The solution is as attached below.

**Acceleration**

At the broader level, we can define the acceleration as the
rate of change of velocity. We can define instantaneous acceleration as the
rate of change of velocity at a very small interval of time which intends to

**0**.
If the velocity is varying uniformly with respect to time,
it’s acceleration is uniform. If velocity is not varying uniformly with respect
to time, it’s acceleration is non uniform and in that case we may need to
integrate the equation to get the actual acceleration.

If a body is having a uniform velocity, it means it is not
having acceleration. All the bodies of the Earth experience acceleration due to
the gravitational force of the Earth and this acceleration is called
acceleration due to gravity.

The numerical value of acceleration due to gravity is
constant and it is equal to 9.8 m/s Squire. It is always directed towards the Center of the Earth and it is due to the mass as well as the size of the Earth.

**Related Posts**

## No comments:

## Post a Comment