Question

A car moving over a straight path, covers
a distance d with constant speed of
40 km/hr and then the same distance with
speed 60 km/hr. The average speed of car
is .........

Answer 1

ANSWER :

Given :

▪ A car covers first half of total distance with speed 40kmph and second half of total distance with speed 60kmph.

To Find :

▪ Average speed of the car.

Concept :

✏ If body covers first half of total distance with speed v1 and second half of total distance with speed v2, then average speed of the body is given by

☞ (v)av = 2v1v2/v1+v2

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

✏ It is a scalar quantity.

Calculation :

→ (v)av = 2v1v2/v1+v2

→ (v)av = 2(40)(60)/(40+60)

→ (v)av = 4800/100

→ (v)av = 48kmph

Answer 2

Given:

A car moving over a straight path, covers  a distance d with constant speed of  40 km/hr and then the same distance with  speed 60 km/hr.

To Find:

Average speed of car for given time interval

Solution:

It is given that,

Firstly, car travelled distance 'd' with velocity 40 km/hr and travelled distance d again with velocity 60 km/hr

So,

Total distance covered by car,

D= d+d= 2d

Let t₁ be the time taken by car to cover distance d with velocity 40 km/hr and t₂ be the taken by car to cover distance d with velocity 60 km/hr

We know that,

$\pink{\boxed{\rm{Average\:Speed=\dfrac{Total\:distance\:covered}{Total\:time\:taken}}}}$

$\purple{\boxed{\bf{Time=\dfrac{Distance}{Speed}}}}$

So,

$\longrightarrow\rm{t_{1}=\dfrac{d}{40}}$

$\longrightarrow\rm{t_{2}=\dfrac{d}{60}}$

Now,

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

$\longrightarrow\rm{Average\:Speed=\dfrac{D}{t_{1}+t_{2}}}$

$\longrightarrow\rm{Average\:Speed=\dfrac{2d}{\dfrac{d}{40}+\dfrac{d}{60}}}$

$\longrightarrow\rm{Average\:Speed=\dfrac{2\cancel{d}}{\cancel{d}\bigg(\dfrac{1}{40}+\dfrac{1}{60}\bigg)}}$

$\longrightarrow\rm{Average\:Speed=\dfrac{2}{\dfrac{60+40}{2400}}}$

$\longrightarrow\rm{Average\:Speed=\dfrac{2\times2400}{100}}$

$\longrightarrow\rm{Average\:Speed=\dfrac{4800}{100}}$

$\longrightarrow\rm\green{Average\:Speed=48\:km/hr}$

Hence, the average speed of car for given time interval is 48 km/hr.