Average velocity and study of formula for average velocity

We already know that the rate of change of position of any object is termed as velocity i.e. velocity is equal to the displacement of object upon given time. So its time for us to define average velocity. It is the given by the mean of velocities taken for traversing a distance in particular time. The average velocity formula will help to find average velocity.

In generic format, the formula for average velocity is given by v = d / t, where d is the total displacement of an object and t is the time elapsed for that displacement. It could contain several small displacements and times. Hence all those distances and times needs to be added respectively and ratio is needed to be taken according to the definition of average velocity.

Steps for finding average velocity:

Consider an object traversing some distance with a variable velocity as shown below. So how to find the average velocity in such case? The following are the steps for finding average velocity.

• Find the instances of displacements like d1, d2, d3 and so on.

• Find the time instances taken for this distances like t1, t2, t3 and so on.

• Now according to the average velocity definition, take the ratio of modulus of sum of distances to the sum of times.

• This is the generic formula for calculating average velocity given as Vavg = |d1 + d2+ d3| / |t1 + t2+ t3|.

Now we know that since velocity is a vector quantity, both magnitude as well as direction are required to define it. The equation for Vavg above gives the magnitude of average velocity.

Until now, we have considered the velocities for linear movement of objects. But what if the objects move in a circular fashion? We need to calculate average angular velocity for that. It can be written as ω = θ / t, where θ is the rotation angle occurred in time t. Common examples where concept of angular velocities come in picture are rotation of fan, wheels etc.

Study of some average velocity examples:

The average velocity examples are given below which will make the topic clear.

(1) Find the average velocity if a object moves 4 m at 2 s and another 10 m at 5 s linearly?

Vavg = |4 + 10| / |2 + 5| = 14 / 7 = 2 m/s.

(2) Find the angular velocity of a minute hand of clock?

Here θ = 2π and time taken by a minute hand to rotate it will be 60 minutes. Hence ω = θ / t = 2π / 60 . Thus ω = 0.104 rad/min.

Average velocity video lesson

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