An ant crawled from a hole to the food. For the first 6 minutes, it travelled at an average speed of 15m/min. For The next 9 minutes it travelles at an average speed of 10m/min what was the average speed of the whole journey?

v = 12 m/min

Explanation:

By definition, the average velocity is the rate of change of the position with respect to time, as follows:

       

Choosing x₀ = 0 and t₀ =0, (1) reduces to :

       

From the givens, we have:

       tif = 6 min + 9 min = 15 min

In order to get xf, we know that during the first part, vavg = 15 m/min, so solving for xf:

       

For the following 9 min, we know that the average speed was 10m/min, so the distance traveled during the second part of the trip was simply:

       

Adding (3) and (4):

       

Replacing xf and tif in (2), we finally get: