Question

The distance between two points A and B is 100m. A person moves from A to B with a speed of 20m/s and from B to A speed of 25m/s . Calculate average speed and average velocity. ​

Answer 1

Answer:

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Answer 2

Given :

• Distance between A and B = 100 m
• Speed from A to B = 20 m/s
• Speed from B to A = 25 m/s

To find :

• Average speed
• Average Velocity

Solution :

Total distance covered in the journey = 2 × Distance between A and B

= 2 × 100

= 200 m

We know that

$\boxed{\sf time \: taken = \dfrac{distance \: travelled}{speed} }$

Time taken when the speed is 20 m/s from A to B

$\sf t_1 = \dfrac{100}{20}$

$\sf \implies t_1 = 5 \: s$

Time taken returning from B to A with speed 25 m/s

$\sf t_{2} = \dfrac{100}{25}$

$\sf \implies t_{2} = 4 \: s$

Total time taken in the whole journey is given by

$\boxed{ \large\sf \: t = t_{1} + t_{2}}$

t = 5+4 t = 9 sec

• The total time taken in the journey is 9 s.

Substituting values in the formula of average speed :

$\boxed{\sf {Average\ speed = {\dfrac{Total\ Distance}{Total\ Time}}}}$

$\sf \: \implies \: average \: speed = \dfrac{200}{9} m {s}^{ - 1}$

$\implies \boxed{\sf \therefore average \: speed \: = 22.23 \: m {s}^{ - 1}}$

Total displacement covered = 100 - 100

= 0 m (as the initial and final points are same)

Average velocity is given by :

Average Velocity = $\sf{ \dfrac{Displacement}{time}}$

$\implies \sf \: average \: velocity = \frac{0}{9}$

$\implies \boxed{ \sf \therefore average \: velocity = 0 \: m {s}^{ - 1} }$