Question

A runner is running around a rectangular track with length 50 meters and width 20 meters with constant speed. If the total time taken by him to run around the complete track is 100 seconds, then determine the following after covering two rounds of this track:

(a) the average speed

(b) the average velocity

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Answer 1

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✤ Required Answer:

✒ GiveN:

• Length of rectangular track = 50 m

• Width of rectangular track = 20 m

• Time taken by runner to complete track = 100 sec

✒ To FinD:

• the average speed after covering two rounds

• the average velocity after covering two rounds

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✤ How to solve?

A runner is running around a rectangular track with length 50 meters and width 20 meters with constant speed. If the total time taken by him to run around the complete track is 100 seconds, then determine the following after covering two rounds of this track: Average speed and Average velocity .

↪ First to understand the question more nicely let's draw the figure . [ See the attachment ]

In order to solve it first we have to find the distance by finding the perimeter of the rectangular track after that we have to find total distance and total time taken... after finding it we can easily find average speed and average velocity by their formula.

Formulas Used to solve this question -

☕ Perimeter :-

$\dag\:\underline{\boxed{\bf{\orange{perimeter=2 \times (l + b)}}}}$

☕ Average speed :-

$\dag\:\underline{\boxed{\bf{\orange{Average \: speed= \frac{total \: distance}{total \: time} }}}}$

☕ Average velocity :-

$\dag\:\underline{\boxed{\bf{\orange{Average \: velocity = \frac{displacement}{total \: time} }}}}$

Now let's solve it !

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✤ Solution :

By using the formula of perimeter the total distance of rectangular track :-

Total distance - 2×(l+b)

➙ 2× ( 50+20 )

➙ 2× ( 70 )

➙ 140 m

Now let's write all we things that we know for round 1 till now

• Distance = 140 m

• Time taken = 100 sec

For round 2 also

• Distance = 140 m

• Time taken = 100 sec

~ Total Distance

➙ 140 × 2

➙ 280 m

~ Total Time taken

➙ 100 × 2

➙ 200 s

Now let's write all we things that we know for total distance and total time till now

• Total distance = 280 m

• total time taken = 200 sec

Now , we know total distance and total time . so, let's calculate the average speed and the average velocity..

★ Average speed :-

$: \Longrightarrow{{\bf{{ \dfrac{total \: distance} { total \: time}}}}}$

$: \Longrightarrow{{{{ \dfrac{280} { 200}}}}}$

$: \Longrightarrow{ \sf\blue{1.4m/s}}$

★ Average velocity :-

$: \Longrightarrow{{\bf{{ \dfrac{displacement} { total \: time}}}}}$

$: \Longrightarrow{{{{ \dfrac{0} { 200}}}}}$

$: \Longrightarrow{ \sf\blue{0m/s}}$

☀️ Hence, solved !!

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Answer 2

Answer:

By using the formula of perimeter the total distance of rectangular track :-

Total distance - 2×(l+b)

➙ 2× ( 50+20 )

➙ 2× ( 70 )

➙ 140 m

Now let's write all we things that we know for round 1 till now

Distance = 140 m

Time taken = 100 sec

For round 2 also

Distance = 140 m

Time taken = 100 sec

~ Total Distance

➙ 140 × 2

➙ 280 m

~ Total Time taken

➙ 100 × 2

➙ 200 s

Now let's write all we things that we know for total distance and total time till now

Total distance = 280 m

total time taken = 200 sec

Now , we know total distance and total time . so, let's calculate the average speed and the average velocity..

★ Average speed :-

: \Longrightarrow{{\bf{{ \dfrac{total \: distance} { total \: time}}}}}:⟹

totaltime

totaldistance

: \Longrightarrow{{{{ \dfrac{280} { 200}}}}}:⟹

200

280

: \Longrightarrow{ \sf\blue{1.4m/s}}:⟹1.4m/s

★ Average velocity :-

: \Longrightarrow{{\bf{{ \dfrac{displacement} { total \: time}}}}}:⟹

totaltime

displacement

: \Longrightarrow{{{{ \dfrac{0} { 200}}}}}:⟹

200

0

: \Longrightarrow{ \sf\blue{0m/s}}:⟹0m/s

☀️ Hence, solved !!

Explanation:

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