Question

A car travel 40km/h at a speed of 80km/h and remaining 40km at a speed of 40km/h. Find the average velocity during whole journey

Answer 1

Correct Question :-

A car travel 40km at a speed of 80km/h and remaining 40km at a speed of 40km/h. Find the average velocity during whole journey

To Find :-

The Average velocity of the car .

Given :-

• Distance $\bf{d_{1} = d_{2} = 40 km}$

• Speed of the car in covering the first 40 km = 80 km/h

• Speed of the car in covering the second 40 km = 40 km/h

We know :-

Average Velocity :–

$\underline{\boxed{\bf{Average\:velocity = \dfrac{d_{1} + d_{2}}{t_{1} + t_{2}}}}}$

Where :-

• d = Displacement

• t = Time Taken

Velocity :–

$\boxed{\underline{\bf{Velocity = \dfrac{s}{t}}}}$

Where :-

• d = Displacement

• t = Time Taken

Concept :-

To Find the Average velocity of the car , first we have to find the time taken in the two different journey's.

Then by applying the formula , we can find the average Velocity of the car.

Solution :-

Time Taken for First JourneY :-

Given :-

• Displacement = 40 km

• Velocity = 80 km/h

Let the time taken be $t_{1}$.

Using the formula and substituting the values in it, we get :-

$:\implies \bf{Velocity = \dfrac{Displacement}{time}} \\ \\ \\ :\implies \bf{80 = \dfrac{40}{t_{1}}} \\ \\ \\ :\implies \bf{80 \times t_{1} = 40} \\ \\ \\ :\implies \bf{t_{1} = \dfrac{40}{80}} \\ \\ \\ :\implies \bf{t_{1} = \dfrac{4}{8}} \\ \\ \\ :\implies \bf{t_{1} = \dfrac{^{1}\not{4}}{^{2}\not{8}}} \\ \\ \\ :\implies \bf{t_{1} = \dfrac{1}{2}} \\ \\ \\ :\implies \bf{t_{1} = 0.5 h} \\ \\ \\ \therefore \purple{\bf{t_{1} = 0.5 h}}$

Hence, the time taken for the first journey is 0.5 h.

Time Taken for Second JourneY :-

Given :-

• Displacement = 40 km

• Velocity = 40 km/h

Let the time taken be $t_{2}$.

Using the formula and substituting the values in it, we get :-

$:\implies \bf{Velocity = \dfrac{Displacement}{time}} \\ \\ \\ :\implies \bf{40 = \dfrac{40}{t_{2}}} \\ \\ \\ :\implies \bf{40 \times t_{2} = 40} \\ \\ \\ :\implies \bf{t_{2} = \dfrac{40}{40}} \\ \\ \\ :\implies \bf{t_{2} = \dfrac{4}{4}} \\ \\ \\ :\implies \bf{t_{2} = \dfrac{^{1}\not{4}}{^{1}\not{4}}} \\ \\ \\ :\implies \bf{t_{2} = \dfrac{1}{1}} \\ \\ \\ :\implies \bf{t_{2} = 1 h} \\ \\ \\ \therefore \purple{\bf{t_{2} = 1 h}}$

Hence, the time taken for the first journey is 1 h.

AveraGe SPeed of the car :-

Given :-

• $\bf{t_{1} = 0.5 h}$

• $\bf{t_{2} = 1 h}$

• $\bf{d_{1} = d_{2} = 40 km}$

Using the formula and substituting the values in it, we get :-

$:\implies \bf{Average\:velocity = \dfrac{d_{1} + d_{2}}{t_{1} + t_{2}}} \\ \\ \\ :\implies \bf{Average\:velocity = \dfrac{40 + 40}{0.5 + 1}} \\ \\ \\ :\implies \bf{Average\:velocity = \dfrac{80}{1.5}} \\ \\ \\ :\implies \bf{Average\:velocity = \dfrac{800}{15}} \\ \\ \\ :\implies \bf{Average\:velocity = 53.3} \\ \\ \\ \therefore \purple{\bf{Average\:Velocity = 53.3 km h^{-1}}}$

Hence, the Average Velocity of the car is 53.3 km/h.

Answer 2

For first half, distance=v1t/2.........for second half, distance=v2t/2

Average speed=v1t/2+v2t/2 the whole divided by t/2+t/2

                   =v1t+v2t/2/t

                   =v1+v2/2

 

                     80+40/2 = 60 km/h