Question

ankit drives at a speed of 20km/h to go to the market but could come back with an average speed of 40km/h calculate the average speed and average velocity for the whole trip

Answer 1

Answer:

Given:

Ankit drives from home to market with 20 km/hr and return to home with 40 km/hr

To find:

• Average speed of whole trip
• Average velocity of whole trip

Concept:

Average speed is defined as the ratio of total distance to the total time taken. Whereas , average velocity is the ratio of displacement to the time taken .

Calculation:

Since starting point and ending points are same for whole trip, displacement is zero. Hence we can say that average velocity is also zero.

For average speed :

$avg. \: v = \dfrac{total \: distance}{total \: time}$

$= > avg. \: v = \dfrac{(d + d)}{ \dfrac{d}{20} + \dfrac{d}{40} }$

Cancelling term d :

$= > avg. \: v = \dfrac{2}{ \dfrac{1}{20} + \dfrac{1}{40} }$

$= > avg. \: v = \dfrac{2}{ \dfrac{(2 + 1)}{40} }$

$= > avg. \: v = \dfrac{40 \times 2}{ 3}$

$= > avg. \: v = \dfrac{80}{ 3}$

$= > avg. \: v = 26.67 \: km {hr}^{ - 1}$

Answer 2

Answer:

• Going Speed = 20 km/hr
• Coming Speed = 40 km/hr
• Let the Fixed Distance be x
• Average Speed & Average Velocity?

$\boxed{\bf{\mid{\overline{\underline{\bigstar\: Average\:Speed\:of\:Trip :}}}}\mid}$

$:\implies\sf Average\:Speed=\dfrac{Total\: Distance}{Total\:Time}\\\\\\:\implies\sf Average\:Speed=\dfrac{Distance+Distance}{Time_1+Time_2}\\\\\\:\implies\sf Average\:Speed=\dfrac{Distance+Distance}{\frac{Distance}{Speed_1}+\frac{Distance}{Speed_2}}\\\\\\:\implies\sf Average\:Speed=\dfrac{x+x}{\frac{x}{20}+\frac{x}{40}}\\\\\\:\implies\sf Average\:Speed=\dfrac{2x}{\frac{2x+x}{40}}\\\\\\:\implies\sf Average\:Speed = \dfrac{2x \times 40}{3x}\\\\\\:\implies\sf Average\:Speed = \dfrac{80}{3}\\\\\\:\implies\underline{\boxed{\sf Average\:Speed= 26.67\:km/hr}}$

⠀

$\therefore\:\underline{\textsf{Average Speed of whole trip is \textbf{26.67 km/hr}}}.$

$\rule{200}{2}$

$\boxed{\bf{\mid{\overline{\underline{\bigstar\: Average\: Velocity\:of\:Trip :}}}}\mid}$

$:\implies\sf Average\: Velocity=\dfrac{Total\: Displacement}{Total\:Time}\\\\{\scriptsize\qquad\bf{\dag}\:\:\text{Starting \& Ending Point of Trip is Same, Hence Displacement = 0}}\\\\:\implies\sf Average\: Velocity=\dfrac{0}{Total\:Time}\\\\\\:\implies\underline{\boxed{\sf Average\: Velocity=0}}$

⠀

$\therefore\:\underline{\textsf{Average Velocity of whole trip is \textbf{0}}}.$