Average Speed

 ‘d’ denotes distance; ‘t’ denotes time. ∆ is a Greek symbol used to denote the difference (∆ is called Delta)

You have the following data from scooter ride about the distance and time taken to complete the journey:

                                                                  Table 3.2:  Scooter Ride

What was the total distance covered during the ride?

Total distance covered, ∆d = d₁ - d₀

                                                = 6 - 0 km
                                                = 6 km 

What was the time taken to cover this distance?

 Time taken to cover this distance, ∆t = t ₁ - t ₀

                                                                   = 15-0 minutes

                                                                   = 15 minutes

 

To calculate the average speed, we divide the total distance covered by the total time taken for the journey.

Speed,   v = Total distance covered / time taken to cover this distance

                       
        
                                                               \(v = {\Delta d \over \Delta t}\)

                                                                   \( = {6~km \over 15~minutes}\)
             
                                                                   \( = \) 0.4 km / minute

What does this number tell us?

We can say that the scooter rider covered the entire journey at the average speed of 0.4 km/minute (0.4 kilometer/minute). we call this the average speed


The instantaneous speed of the scooter was changing throughout the 6 km journey. You know now that that the cooter took 15 minutes to cover this journey.


The average speed of an object gives us a rough idea about how fast or slow an object is traveling. It helps us to estimate or predict the future trends of the motion, which we often do on the daily basis. 


 

The Average Speed helps us to estimate future trends of the motion.

Let us take another example to understand what an average speed is. The distance to a nearby town is 60km. A bus takes two hours to cover the distance. We can use the motion equation, that we just worked out above, to find out that the average speed of the bus is 30km/hour.

So if you just know the average speed, the total distance of 60 km and do not know the time, we could now safely assume that it will take us two hours to reach the town. Of course, sometimes it may take a little more time if the bus halts many times along the route. Or it may take less time if the driver drives faster.