Question:

A train travels from one station to another at a speed of $40\, km/hour$ and returns to the first station at a speed of $60\, km/hour$. The average speed and average velocity of the train are respectively

Updated On: Jul 6, 2022
  • $48 \,km \,hr^{-1}, 0$
  • $0, 48 \,km \,hr^{-1}$
  • $50\, km \,hr^{-1}$, $50\, km \,hr^{-1}$
  • $50\, km \,hr^{-1}, 0$
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The Correct Option is A

Solution and Explanation

Let S be the distance between two stations Time taken by train from one station to another,$t_1 = \frac{S}{40}$ hr. Time taken for returning, $t_2 = \frac{S}{60}$ hr. Average speed = $\frac{Total \, distance}{Total \, time} = \frac{S+S}{\frac{S}{40} + \frac{S}{60}}$ = 48 km $hr^{-1}$ Average velocity = $\frac{Displacement}{time} = \frac{0}{time} = 0$ * Shortcut Average speed = $\frac{2\upsilon_1 \upsilon_2}{\upsilon_1 + \upsilon_2} = \frac{2(40 \times 60)}{40 + 60 } $ 48 km $hr^{-1}$
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Notes on Motion in a straight line

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:

  1. 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.
  2. 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.