Question

A train travels with a speed of 60 km h-' from
station A to station B and then comes back with a
speed 80 km h- from station B to station A. Find :
(i) the average speed, and (ii) the average velocity
of train.
Ans. (i) 68.57 km h-, (ii) zero​

Answer 1

Answer:

(i) $v_{avg} = 68.57 kmph$

(ii) $V_{avg}= 0$

Explanation:

Given

A train travels with a speed 60 Km/h from A to B

v1 = 60 km/h

Also, it travels from B to A , with a speed 80 km/h

v2 = 80 km/h

To Find

(i) Average speed

(ii) Average velocity

Solution

Average speed

$v_{avg} = \dfrac{2v_{1} v_{2}}{v_{1} + v_{2}}$

$v_{avg} = \dfrac{2(60)(80)}{60+80}$

$v_{avg} = \dfrac{9600}{140}$

$v_{avg} = 68.57 kmph$

Average velocity

$V_{avg}= <strong>\</strong><strong>dfrac{</strong><strong>d</strong><strong>i</strong><strong>s</strong><strong>p</strong><strong>l</strong><strong>a</strong><strong>c</strong><strong>e</strong><strong>m</strong><strong>e</strong><strong>n</strong><strong>t</strong><strong>}</strong><strong>{</strong><strong>time</strong><strong>}</strong>$

$V_{avg}= \dfrac{0}{time}$

$V_{avg}= 0$

___________________

$\mathbb{\pink{Note:-}}$

➡Since, the train travels from A to B and returns to A. DISPLACEMENT = 0

➡ "V" represents Velocity and $v$ represents Speed

Answer 2

$\mathfrak{\huge{\red{\underline{\underline{AnswEr :}}}}}$

» Average Speed = 68.57 km/hr

» Average Velocity = 0

$\mathfrak{\huge{\red{\underline{\underline{ExplanaTion :}}}}}$

Given :

A train travels with a Speed of 60 km/hr from Station A to Station B and with a Speed of 80km/hr from Station B to Station A.

Let

⚘ Distance = Constant

⚘ Speed1 (x) = 60km/hr

⚘ Speed2 (y) = 80km/hr

Find :

1. The Average Speed of Train

2. The Average Velocity of Train

Solution :

1] When the Distance is Constant then the Average Speed is Equivalent to Twice of Product of Speed1 and Speed 2 Upon Sum of Speed1 and Speed2

$\huge\boxed{ A.S. = \frac{2xy}{x + y} }$

$\large {A.S. = \frac{2 \times 60 \times 80}{60 + 80}}$

$\large {A.S. = \frac{2 \times 60 \times 80}{140}}$

$\large {A.S. = \frac{480}{7}}$

$\large {A.S. = 68.57 \: km/hr}$

$\mathscr\pink{Average\:Speed\:=\:68.57\:km/hr}</p><p>$

2] Average Velocity is equivalent to Rate of Displacement.

$\huge \boxed{A.V. = \frac{Displacement}{Time} }$

$\large{A.V. = \frac{0}{t}}$

» As Displacement is Zero Here Because Train Traveled Back to its Initial Point.

$A.V. = 0$

$\mathscr\pink{Average\:Velocity \:=\:Zero(0)}</p><p>$