Question

Ramesh travels 80 km at the speed of 40 Km/h and then another 80 km at 60 km/h. What is his average speed?

Answer 1

First of all, let's learn the definition of Average Speed :

Average Speed is defined as the ratio of total distance to the total time taken to cover that distance.

Since the definition involves distance , Average Speed is an scalar quantity having only magnitude and no direction.

Calculation:

$avg. \: v = \dfrac{total \: distance}{total \: time}$

$= > avg. \: v = \dfrac{(80 + 80)}{( \frac{80}{60} + \frac{80}{40} )}$

$= > avg. \: v = \dfrac{160}{( \frac{80}{60} + \frac{80}{40} )}$

Cancelling common values :

$= > avg. \: v = \dfrac{ \cancel{160}}{( \frac{ \cancel{80}}{60} + \frac{ \cancel{80}}{40} )}$

$= > avg. \: v = \dfrac{2}{( \frac{1}{60} + \frac{1}{40} )}$

$= > avg. \: v = \dfrac{2}{( \frac{2 + 3}{120} )}$

$= > avg. \: v = \dfrac{2 \times 120}{5}$

$= > avg. \: v = 48 \: km {hr}^{ - 1}$

So final answer :

Average Speed is 48 km/hr.

Answer 2

▶ Solution :

Given :

▪ Ramesh travels first half (80km) of the total distance at the speed of 40kmph and second half (80 km) of the total distance at the speed of 60kmph.

To Find :

▪ Average speed of ramesh.

Concept :

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

✏ It is a scalar quantity.

✏ It has only magnitude.

✴ If a body covers first half of the total distance at the speed of V1 and second half of the total distance at the speed of V2, then average speed of the body is given by

☞ Vav = 2V1V2/(V1 + V2)

Calculation :

→ Vav = 2V1V2/(V1 + V2)

→ Vav = 2(40)(60)/(40+60)

→ Vav = 4800/100

→ Vav = 48kmph

✒ Formula derivation :

⏭ Let body covers first d distance at the speed of V1 and second d distance at the speed of V2.

๏ Total distancs travelled = 2d

๏ Total time taken = t1 + t2

→ Vav = 2d / (t1 + t2)

We know that,

time = distance/speed

→ Vav = 2d / [(d/V1) + (d/V2)]

→ Vav = 2d(V1V2) / [d(V1 + V2)]

→ Vav = 2V1V2/(V1+V2)