Question

under what condition, the average speed is equal to the magnitude of the average velocity,justify your answer.​

Answer 1

Answer:

First let's define each of the term :

Average speed is defined as the ratio of total distance to the total time taken.

$\boxed{ \red{avg. \: speed = \dfrac{total \: distance}{total \: time} }}$

Average velocity is defined as the ratio of total displacement to the total time taken

$\boxed{ \blue{avg. \: speed = \dfrac{total \: displacement}{total \: time} }}$

Hence there is only 1 condition in which average Velocity and average Speed will be same. It's possible only when the distance and displacement of the object is same in the specified time interval.

And same distance and displacement is possible only when the object is following linear(straight) motion and moving in a single direction.

Answer 2

Answer:

Average Speed : Total Distance travelled by body or object divided by Total Time taken to cover that Distance. It is Scalar Quantity.

$\bigstar\:\boxed{\sf Average\:Speed=\dfrac{Total\: Distance}{Total\:Time}}$

Average Displacement : Total Displacement covered by body or object divided by Total Time taken. It is Vector Quantity.

$\bigstar\:\boxed{\sf Average\: Velocity=\dfrac{Total\: Displacement}{Total\:Time}}$

$\rule{150}{1}$

$\underline{\bf{\dag}\:\textbf{Possible Condition :}}$

This Condition is Possible when Total Distance travelled equals to Net Displacement of Body or Object.

⠀⠀⠀⠀⠀⠀⠀⠀⠀This happens when Body or Object travels along a straight line in a fixed direction.

$\star\:\underline{\boxed{ \green{\sf Total\: Distance=Total\: Displacement}}}$