Question

A car travells a distance with a speed of 50 km /hr and returns with a speed of 40km/hr. Calculate the average speed for the whole journey . In km/hr

Answer 1

Explanation:

Given :-

Speed in the forward direction, v₁ = 50 km/h

Speed during the return journey, v₂ = 40 km/h

To Calculate :-

Average speed, v(avg) = ??

Formula to be used :-

v(avg) = Total distance/Total time taken

Solution :-

Now, in this case we are neither given the total distance nor the total time taken.

Let us say the distance traveled in the forward direction be x

Total distance, d = x + x = 2x

Time taken during forward journey, t₁ = x/50 h

Time taken during the return journey, t₂ = x/40 h

Total time taken, t = x/50 + x/40 = 9x/200 h

Now,

v(avg) = Total distance/Total time taken

⇒ v(avg) = 2x/9x/200

⇒ v(avg) = 2x × 200/9x

⇒ v(avg) = 400/9

⇒ v(avg) = 44.44 km/h

Hence, the average speed of the whole journey is 44.44 km/h.

Answer 2

Given :

▪ A car travells a distance with a speed of 50kmph and returns with a speed of 40kmph.

To Find :

▪ Average speed of car during the whole journey.

SoluTioN :

↗ If a particle moves a distance at speed V_1 and comes back with speed V_2, then

$\bigstar\:\underline{\boxed{\bf{\red{V_{av}=\dfrac{2V_1V_2}{V_1+V_2}}}}}$

but $\bf{\vec{V}_{av}=0}$

$\dashrightarrow\sf\:V_{av}=\dfrac{2(40)(50)}{40+50}\\ \\ \dashrightarrow\sf\:V_{av}=\dfrac{4000}{90}\\ \\ \dashrightarrow\underline{\boxed{\bf{\blue{V_{av}=44.44\:kmph}}}}\:\orange{\bigstar}$