Average Velocity And Average Speed

Let the total distance be

D

. The car covers the first third of the distance (

D%2F3

) at 10 km/h, the second third at 20 km/h, and the last third at 60 km/h. - Time taken for the first third:

t_1%20%3D%20%5Cfrac%7BD%2F3%7D%7B10%7D

- Time taken for the second third:

t_2%20%3D%20%5Cfrac%7BD%2F3%7D%7B20%7D

- Time taken for the last third:

t_3%20%3D%20%5Cfrac%7BD%2F3%7D%7B60%7D

Total time taken:

t_%7B%5Ctext%7Btotal%7D%7D%20%3D%20t_1%20%2B%20t_2%20%2B%20t_3%20%3D%20%5Cfrac%7BD%2F3%7D%7B10%7D%20%2B%20%5Cfrac%7BD%2F3%7D%7B20%7D%20%2B%20%5Cfrac%7BD%2F3%7D%7B60%7D

Simplify:

t_%7B%5Ctext%7Btotal%7D%7D%20%3D%20%5Cfrac%7BD%7D%7B30%7D%20%2B%20%5Cfrac%7BD%7D%7B60%7D%20%2B%20%5Cfrac%7BD%7D%7B180%7D

t_%7B%5Ctext%7Btotal%7D%7D%20%3D%20%5Cfrac%7B6D%7D%7B180%7D%20%2B%20%5Cfrac%7B3D%7D%7B180%7D%20%2B%20%5Cfrac%7BD%7D%7B180%7D%20%3D%20%5Cfrac%7B10D%7D%7B180%7D%20%3D%20%5Cfrac%7BD%7D%7B18%7D

Average speed is given by:

%5Ctext%7BAverage%20speed%7D%20%3D%20%5Cfrac%7B%5Ctext%7BTotal%20distance%7D%7D%7B%5Ctext%7BTotal%20time%7D%7D%20%3D%20%5Cfrac%7BD%7D%7B%5Cfrac%7BD%7D%7B18%7D%7D%20%3D%2018%20%5C%2C%20%5Ctext%7Bkm%2Fh%7D

Chapter Questions
1 MCQs