Question

A bus travels a distance of 180 km with a speed of 60 km/hr and returns with the speed of 30 km/hr. Calculate the average speed and average velocity for the entire journey

Answer 1

Given:

A bus travels a distance of 180 km with a speed of 60 km/hr and returns with the speed of 30 km/hr

To Find:

Average speed  and average velocity of bus for the entire journey

Solution:

Total Journey= 180+180= 360km

We know that,

$\longrightarrow\bf{Time=\dfrac{Distance}{Speed}}$

$\longrightarrow\bf{Average\:Speed=\dfrac{Total\:distance\:covered}{Total\:time\:taken}}$

$\longrightarrow\bf{Average\:Velocity=\dfrac{Total\:displacement}{Total\:time\:taken}}$

Let t₁ hr be the time taken by bus to reach the destination and t₂ hr be the time taken by bus to return to starting point from destination

So,

$\longrightarrow\mathrm{t_{1}=\dfrac{180}{60}=3\:hr}$  

$\longrightarrow\mathrm{t_{2}=\dfrac{180}{30}=6\:hr}$

Now,

$\longrightarrow\sf{Average\:Speed\:of\:Bus=\dfrac{Total\:distance\:covered}{Total\:time\:taken}}$

$\longrightarrow\sf{Average\:Speed\:of\:Bus=\dfrac{360}{t_{1}+t_{2}}}$

$\longrightarrow\sf{Average\:Speed\:of\:Bus=\dfrac{360}{3+6}}$

$\longrightarrow\sf{Average\:Speed\:of\:Bus=\dfrac{360}{9}}$

$\longrightarrow\sf\pink{Average\:Speed\:of\:Bus=40\:km/hr }$

Since, bus has returned to the starting point.

∴ Total displacement= 0

$\longrightarrow\sf{Average\:Velocity\:of\:Bus=\dfrac{Total\:displacement}{Total\:time\:taken}}$

$\longrightarrow\sf{Average\:Velocity\:of\:Bus=\dfrac{0}{t_{1}+t_{2}}}$

$\longrightarrow\sf\purple{Average\:Velocity\:of\:Bus=0\:km/hr}$

Answer 2

Given

● Bus travels distance of 180 km.

● Speed while going = 60 km/h

● Speed while returning = 30 km/h

To find

● Average speed & average velocity.

Solution

As the bus goes & returns to the same point, so it covers the same distance twice.

Using speed formula :

⋆ Speed = Distance/Time

⇒ 60 = 180/Time

⇒ 60 × Time = 180

⇒ Time = 180/60

⇒ Time = 3 hours.

∴ Time taken by bus to go = 3 hours.

Using the same formula again :

⋆ Speed = Distance/Time

⇒ 30 = 180/Time

⇒ 30 × Time = 180

⇒ Time = 180/30

⇒ Time = 6 hours.

∴ Time taken by bus to return = 6 hours.

Now using the formula :

⋆ Av.speed = Total distance/Total time

⇒ Av. speed = (180 + 180)/(3 + 6)

⇒ Av. speed = 360/9

⇒ Av. speed = 40 km/h

∴ Average speed of bus = 40 km/h (Ans.)

____________________________

Again using the formula :

⋆ Av. velocity = Total displacement/Total time

As the bus goes to a point & comes back to same point, so total displacement of bus remains 0.

Putting values in the formula now :

⇒ Av. velocity = 0/(3 + 6)

⇒ Av. velocity = 0/9

⇒ Av. velocity = 0 km/h

∴ Average velocity of bus = 0 km/h (Ans.)