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

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 (A) 48 km hr-1, 0 (B) 0, 48 km hr-1 (C) 50 km hr-1, 50 km hr-1 (D) 50 km hr-1, 0

Tardigrade Admin · Accepted Answer

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{T o t a l d i s t an ce}{T o t a l t im e} = \frac{S + S}{\frac{S}{40} + \frac{S}{60}}

= 48 km

h r^{- 1}

Average velocity =

\frac{D i s pl a ce m e n t}{t im e} = \frac{0}{t im e} = 0

* Shortcut Average speed =

\frac{2 υ _{1} υ _{2}}{υ _{1} + υ _{2}} = \frac{2 ( 40 \times 60 )}{40 + 60}

48 km

h r^{- 1}

Q. A train travels from one station to another at a speed of $40 km / h o u r$ and returns to the first station at a speed of $60 km / h o u r$ . The average speed and average velocity of the train are respectively

$48 km h r^{- 1}, 0$

$0, 48 km h r^{- 1}$

$50 km h r^{- 1}$ , $50 km h r^{- 1}$

$50 km h r^{- 1}, 0$

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

48kmhr−1,0

0,48kmhr−1

50kmhr−1, 50kmhr−1

50kmhr−1,0

Q. A train travels from one station to another at a speed of $40 km / h o u r$ and returns to the first station at a speed of $60 km / h o u r$ . The average speed and average velocity of the train are respectively

$48 km h r^{- 1}, 0$

$0, 48 km h r^{- 1}$

$50 km h r^{- 1}$ , $50 km h r^{- 1}$

$50 km h r^{- 1}, 0$