Question

A vehicle travels half the distance L with speed V₁ and the other half with speed V₂, then its average speed is ______.

Options

• `(V_1 + V_2)/2`

• `(2V_1 + V_2)/(V_1 + V_2)`

• `(2V_1 V_2)/(V_1 + V_2)`

• `(L(V_1 + V_2))/(V_1V_2)`

Answer 1

A vehicle travels half the distance L with speed V₁ and the other half with speed V₂, then its average speed is `underline((2V_1 V_2)/(V_1 + V_2))`.

Explanation:

Consider the diagram below in which motion is as shown below.

Let the vehicle travels from A to B. Distances, velocities and time have taken are shown. To calculate average speed we will calculate the total distance covered and will divide it by the time interval in which it covers that total distance.

Time taken to travel first half distance `t_1 = (L/2)/v_1 = L/(2v_1)`

Time taken to travel second half distance `t_2 = L/(2v_2)`

Total time = t₁ + t₂

= `L/(2v_1) + L/(2v_2)`

= `L/2 [1/v_1 + 1/v_2]`

We know that

v_av = Average speed

= Total distance/Total time

`v_(av) = L/(L/2[1/v_1 + 1/v_2])`

= `(2v_1v_2)/(v_1 + v_2)`

Important point: Students usually thought that `v_(av) = (v_1 + v_2)/2` but it is not the average speed when two equal distances are covered by speeds v₁ and v₂.

Remember: If t₁ = t₂ = t, then `v_(av) = (v_1 + v_2)/2`. Average speed is equal to the arithmetical mean of individual speeds. (if the particle moves in equal intervals of time at different speeds v₁ and v₂).

And also we should not confuse distance and displacement. Distance ≥ Displacement.