Question

A vehicle travels from A to B at a constant speed of 60 km/hr and returns from B to A at a constant speed of 40 km/hr.Find average speed and average velocity.

Answer 1

Given :-

◉ A vehicle travels from A to B at a constant speed of s₁ = 60 km/hr and returns from B to A at a constant speed of s₂ = 40 km/hr.

To Find :-

◉ Average speed and Average velocity

Solution :-

Let the distance travelled by the vehicle be d.

A to B

We have,

• Distance travelled = d
• Speed, s₁ = 60 km/hr

Let us find the time taken,

⇒ Time taken = Distance / Speed

⇒ t₁ = d / 60 ...(1)

B to A

We have,

• Distance travelled = d
• Speed, s₂ = 40 km/hr

Similarly,

⇒ Time taken = Distance / Speed

⇒ t₂ = d / 40 ...(2)

Now, Let us find the average speed,

⇒ Average speed = Total distance / Total time

⇒ Avg. speed = (d + d) / (d/60 + d/40)

⇒ Avg. speed = 2d / ( 2d + 3d/120 )

⇒ Avg. speed = 120×2d / 5d

⇒ Avg. speed = 240 / 5

⇒ Avg. speed = 48 km/hr

Here, The displacement of the vehicle is zero because the vehicle returned back to its initial position i.e., A so average velocity would be zero.

Answer 2

$\large{\boxed{\bf{AnswEr}}}$

• Average speed = 48 km/hr

• Average velocity = 0

Given :-

• A vehicle travels from A to B at a constant speed of 60 km/hr.

• Returns from B to A at a constant speed of 40 km/hr.

To Find :-

• Average speed and average velocity.

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$\large{\boxed{\bf{Solution}}}$

★ Statement of the given problem :-

➪ A vehicle travels from A to B at a constant speed of 60 km/hr and returns from B to A at a constant speed of 40 km/hr.Find average speed and average velocity.

★ Basic assumptions :-

• Let D denotes the distance (in km) between A and B.

• Let S denotes the average speed (in km/hr) over the entire journey of the vehicle.

• Let V denotes the average velocity (in km/hr) over the entire journey of the vehicle.

★ Hence, from the above data, we get as follows,

S = total distance travelled/ total travelled time .....1)

V = total travelled displacement/ total travelled time .....2)

From 1) we get,

S = { D + D / (D/40 + D/60) }

➪ S = 2/1/24

➪ S = 48 km/hr

From 2) we get,

V = { D - D / (D/40 + D/60) }

➪ V = {0 / ( D/40 + D/60) }

➪ V = 0 km/hr

Hence, average speed = 48km/hr and average velocity = 0 respectively.

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