Question:
A bus travelling the first one-third distance at a speed of ${10 \, km \, h^{-1}}$, the next one-third at ${20 \, km \, h^{-1}}$ and last one third at ${60 \, km \, h^{-1}}$. The average speed of bus is
A bus travelling the first one-third distance at a speed of ${10 \, km \, h^{-1}}$, the next one-third at ${20 \, km \, h^{-1}}$ and last one third at ${60 \, km \, h^{-1}}$. The average speed of bus is
Updated On: Jun 7, 2022
- ${16 \, km \, h^{-1}}$
- ${18 \, km \, h^{-1}}$
- ${9 \, km \, h^{-1}}$
- ${48 \, km \, h^{-1}}$
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The Correct Option is B
Solution and Explanation
Here $v_1 = {10\, km\, h^{-1} for \, 1^{st} \, 1/3^{rd} \, distance}$
$v_2 = {20\, km\, h^{-1} for \, 2^{nd} \, 1/3^{rd} \, distance}$
$v_3 = {60\, km\, h^{-1} for \, 3^{rd} \, 1/3^{rd} \, distance}$
$v_{avg} = \frac{3 v_1 v_2 v_3}{v_1 v_2 + v_2 v_3 + v_3 v_1}$
$= \frac{3 \times 10 \times 20 \times 60}{10 \times 20 + 20 \times 60 + 60\times 10} $
$v_{avg} ={18 \, km \, h^{-1}}$
$v_2 = {20\, km\, h^{-1} for \, 2^{nd} \, 1/3^{rd} \, distance}$
$v_3 = {60\, km\, h^{-1} for \, 3^{rd} \, 1/3^{rd} \, distance}$
$v_{avg} = \frac{3 v_1 v_2 v_3}{v_1 v_2 + v_2 v_3 + v_3 v_1}$
$= \frac{3 \times 10 \times 20 \times 60}{10 \times 20 + 20 \times 60 + 60\times 10} $
$v_{avg} ={18 \, km \, h^{-1}}$
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Concepts Used:
Motion in a straight line
The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion.
Types of Linear Motion:
Linear motion is also known as the Rectilinear Motion which are of two types:
- Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
- Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.