Question

A train travels from one station to another station at an average speed of 40km/h and returns back to the first station at an average speed of 60km/h. Find the average speed and average velocity of the train? Ignore the stoppage time at second station.​

Answer 1

ANSWER :

Given :

▪ A train travels from one station to another station at an average speed of 40kmph and returns back to the first station at an average speed of 60kmph.

To Find :

▪ Average speed of train.

▪ Average velocity of train.

Concept :

☞ Average speed is defined as the ratio of total distance travelled to the total time taken.

☞ It is a scalar quantity.

☞ Average velocity is defined as the ratio of total displacement to the total time taken.

☞ It is a vector quantity.

☞ The total actual length of path is called as distance.

☞ The shortest distance b/w initial and final point of the whole journey is called as displacement.

Calculation :

✒ Average speed :

→ Av.speed = 2v1v2/(v1+v2)

→ Av.speed = 2(40)(60)/(40+60)

→ Av.speed = 4800/100

→ Av.speed = 48kmph

✒ Average velocity :

→ Av.velocity = displacement/time

Displacement = Δposition = 0

(i.e. train returns to the initial point)

→ Av.velocity = zero

Answer 2

Given :

• A train travels from one station to another station at an average speed of 40km/h

• The train returns back to the first station at an average speed of 60km/h.

To Find :

• Average Speed of the train

• Average Velocity of the train

Solution :

Let the Distance between Station A to Station B be x km

After returning of Train Distance will be x + x = 2x km

Till now we've :

• Total Distance = 2x

• Displacement = 0

Now,

Time taken to reach from one station to another by the train :

★ Time = Distance/Speed

→ $\: \sf\: Time_{1}$ = x/40 hrs

Time taken to return back at the first station by the train :

★ Time = Distance/Speed

→ $\: \sf\: Time_{2}$ = x/60 hrs

Total Time Taken : $\: \sf\: Time_{1}\: + Time_{2}$

→ x/40 + x/60

→ 3x + 2x/120

→ 5x/120

→ x/24 hrs

• Let's find Average Speed First :

★ Average Speed = Total Distance Covered/Total Time Taken

→ 2x/x/24

→ 2x × 24/x

→ 24 × 2

→ 48 km/hr

$\therefore$ Average Speed of the train is 48 km/hr

• Let's find Average Velocity now :

★ Average Velocity = Total Displacement Covered/Total Time Taken

→ 0/x/24

→ 0 × 24/x

→ 0/x

→ 0 km/hr

$\therefore$ Average Velocity of the train is 0 km/hr.