Question

2. (a) Define average speed (b) A bus travels a distance of 120km with a speed of 40km/h and returns with a speed of 30km/h . Calculate average speed for the entire journey

Answer 1

•$\LARGE{ \underline{ \underline{ \bold{ \orange{ Your \: answers}}}}}$

1) Average speed is defined as the total distance travelled by total time taken. It is the uniform speed the body might have travelled the same distance in same duration. So, it can be written as:

$\large \purple{ \boxed{ \rm{Avg. \: speed = \frac{Total \: distance \: travelled}{Total \: time \: taken} }}}$

So, We have to keep in mind that for any numerical problem, we need to find the total distance and total time in order to find the average speed.

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2) GiveN:

• A bus travels to and fro covering 120 km twice.
• While going, speed is 40 km/h and while returning speed is 30 km/h

To FinD:

• Average speed of the bus in the journey.

How to solve?

We can solve this question by using the above formula, but we can see that time is not given here. So, if we write the same formula in a different way, it will be

$\large{ \boxed{ \rm{\purple{Time = \frac{Distance}{Speed} }}}}$

Because, we known that speed is rate of distance travelled and then, time = distance/time. So, by using this let's solve the question.

Solution:

Total distance travelled = 120 km + 120 km = 240 km

Total time taken = Time taken while going + Time taken while returning

• Time while going = 120/40 hr
• Time while returning = 120/30 hr

So, Total time taken = 120/40 hr + 120/30 hr

By using formula of Avg. speed,

$\large{ \rm{ \longrightarrow \: Avg. \: speed = \frac{120 + 120 \: km}{ \frac{120}{40}h + \frac{120}{30}h } }} \\ \\ \large{ \rm{ \longrightarrow \: Avg. \: speed = \frac{240 \: km}{3h + 4h} }} \\ \\ \large{ \rm{ \longrightarrow \: Avg. \: speed = \frac{240 \: km}{7h} }} \\ \\ \large{ \rm{ \longrightarrow \: Avg. \: speed \approx \: \boxed{ \red{34.285 \: km {h}^{ - 1} }}}} \\ \\ \large{ \therefore{ \rm{ \underline{ \underline{ \purple{Hence \: solved \: \dag}}}}}}$

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Answer 2

${ \purple{ \boxed{ \underline{ \mathtt{Question \: 1 }}}}}$

Define average speed.

${ \purple{ \boxed{ \underline{ \mathtt{Answer \: 1}}}}}$

The average speed of an object is the total distance traveled by the object divided by the elapsed time to cover that distance.

⇒ It's a scalar quantity which means it is defined only by magnitude.

$s = \frac{d}{t}$

• s= speed
• d=distance
• t=time

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${ \purple{ \boxed{ \underline{ \mathtt{Question \: 2}}}}}$

A bus travels a distance of 120km with a speed of 40km/h and returns with a speed of 30km/h . Calculate average speed for the entire journey.

${ \purple{ \boxed{ \underline{ \mathtt{Answer \: 2}}}}}$

${ \bold{ \underline{ \bf{Given}}}}$

• Distance = 120 km
• Speed= 40 km / hr

$speed = \frac{distance}{time}$

$time = \frac{distance}{speed}$

$= \frac{120}{40}$

• Time =3 hour

For return of train

• Distance = 120 km
• Dpeed = 30 km/ hr
• Time = 4 hr

${ \green{ \boxed{ \bf{average \: speed \: = \frac{total \: distance}{total \: time \: taken}}}}}$

➟$\frac{(120) + (120)}{(3) + (4)}$

➟$\frac{240}{7}$

➟${ \boxed{ \bf{34.2km \: per \: hour}}}$

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