Average Speed Calculation-Question

A particle moves one third of the distance with a speed of 3 ms^-1 .Then it moves one fifth of the remaining distance with a speed 2 ms^-1 and the remaining final distance with a velocity 5 ms^-1 What is the average speed of the particle throughout the journey ?

Solution:

$${Average \ speed =\frac{Total \ distance \ travelled}{Total \ time \ taken}}$$

Total distance = d

Total time taken $${t=t_1+t_2+t_3}$$

Total time taken $${t=\frac{d}{9} +\frac{d}{15}+\frac{8d}{75}}$$

$${t=\frac{64d}{225}}$$

$${Average \ speed =\frac{d}{\frac{64d}{225}}}$$

$${Average \ speed =\frac{225}{64}}$$

$${Average \ speed =3.52 \ \frac{m}{s}}$$

Links to this post

Average Speed Calculation: 3/4th and 1/4th Distance

Average Speed Calculation: Distance, Time, and Velocity