Question

Q2) A car goes from station A to B, with a speed of 40km/h and returns from B to A with a speed of 80km/h. Find the average speed and average velocity of the car.
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Answer 1

Answer :-

→ Average speed of the car is 53.33 km/h .

→ Average velocity of the car is 0 km/h .

Explanation :-

We have :-

• Speed from A to B (v₁) = 40 km/h

• Speed from B to A (v₂) = 80 km/h

______________________________

For average speed :-

In this case, the car goes from A to B and then returns back from B to A .

So, distance travelled by the car is same in both cases.

In this situation, average speed is given by :-

2v₁v₂/(v₁ + v₂)

= (2 × 40 × 80)/(40 + 80)

= 6400/120

= 53.33 km/h

For average velocity :-

The car starts from the point A and moves to B . Thereafter, it again moves from B to A .

So, initial and final points of the car are same.

Thus, displacement is zero .

Also let time taken be 't' .

Average velocity :-

= Total displacement/Total time

= 0/t

= 0 km/h

Answer 2

$\red{\bigstar}$ G I V E N

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• A car goes from station A to B, with a speed of 40 km/h

• Returns from B to A with a speed of 80 km/h

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$\blue{\bigstar}$ T OㅤF I N D

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• Average speed and average velocity of the car?

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$\purple{\bigstar}$ S O L U T I O N

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• Let the distance b/w A and B be x km

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$\sf \dashrightarrow \: Time\:taken\:to\:cover\:distance\:from\:A\:to\:B = \dfrac{x}{40}$

$\\ \sf \dashrightarrow \: Time\:taken\:to\:return\:from\:B\:to\:A = \dfrac{x}{80}$

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Now,

$\:$

$\sf \quad \dashrightarrow \quad Average\:speed = \dfrac{x + x}{ \dfrac{x}{40} + \dfrac{x}{80}}$

$\\ \sf \quad \dashrightarrow \quad Average\:speed = \dfrac{2x}{ \dfrac{2x + x}{80} }$

$\\ \sf \quad \dashrightarrow \quad Average\:speed = \dfrac{2x}{ \dfrac{3x}{80} }$

$\\ \sf \quad \dashrightarrow \quad Average\:speed = 2x\:\times\: \dfrac{80}{3x}$

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After cancelling 'x' with 'x', we get ::

$\\ \sf \quad \dashrightarrow \quad Average\:speed = \dfrac{2\:\times\:80}{3}$

$\\ \sf \quad \dashrightarrow \quad Average\:speed = {\cancel{\dfrac{160}{3}}}$

$\\ \sf \quad \dashrightarrow \quad \pink{Average\:speed = 53.33\:km/h}$

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• Initial and final positions are same. So, total displacement becomes zero (Average velocity = Total displacement/Total time taken = 0/t = 0 km/h). Hence, average velocity is also zero.

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$\orange{\bigstar}$ H E N C E

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• Average speed = 53.33 km/h

• Average velocity = 0 km/h

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$\green{\bigstar}$ F O R M U L A EㅤU S E D

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• $\small \sf Time = \dfrac{Distance}{Speed}$

• $\small \sf Average\:speed = \dfrac{Total\:distance\:covered}{Total\:time\:taken}$

• $\small \sf Average\:velocity = \dfrac{Total\:displacement}{Total\:time\:taken}$

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