AVERAGE VELOCITY FORMULA

Question

We sometimes calculate average velocity as follows

v1+v2/2 i.e addition of all velocities divided by number of velocities.

1. In the denominator, do we divide it by total time or the number of velocities given(just like we calculate normal average).
2. why cant we calculate average speed or velocity if like for eg v1,v2,v3 are given and like v1+v2+v3/3. why isnt this applicable sometimes plz explain with example would be great help. thank you. also answer the first question. thank you.

Answer 1

You are absolutely right -- (v₁+v₂)/2 practically never gives you the average velocity.

And you are also right that we need to divide by time, not number of velocities.

It is not possible to calculate average velocity of v₁ and v₂ without knowing how long they applied.

This is one proper way:

Suppose you travel at velocity v₁ for time t₁,

then you travel at velocity v₂ for time t₂.

Then the average velocity is

(v₁t₁ + v₂t₂)/(t₁ + t₂)

In general, average velocity is always DISTANCE/TIME.

One must also be very careful when the travel is not in the same direction.

Then we must take into account that velocities are vectors and (v₁t₁ + v₂t₂) is vector addition.

As a simply example, suppose you drive at 55mph for some time, then you get out of your car and make a few steps at 5mph.

Nobody would say that your average speed was 30mph.

To calculate average speed you need to know how long you travelled at 55mph.