Answer to Question #93574 in Mechanics | Relativity for Shirshak Aryal

Question

A body moves from A to B at 40 km/hr and returns from B to A at 60 km/hr. Calculate the average speed and average velocity of the body during the total trip.

Answer 1

It took t₁ time for car to travel from point A to point B and t2 time to travel from point B to point A. Consequently, it took t₁+t₂ for the car to make its movement.

Velocity is displacement done, divided by time it took to make this displacement. Displacement is the distance between starting and ending points of movement. The car started its movement at point A, than travelled to point B, than travelled to point A and finished its movement. Therefore, the starting point is A and the finishing point is A. Distance between point A and point A is 0. Thus, the displacement is 0. Thus, the average velocity is $V=\dfrac{displacement}{t_1+t_2}=\dfrac{0}{t_1+t_2}=0$

The distance between point A and point B is x. Let mark the speed of car while travelling from point A to point B as S₁=40 km/hr and from point B to point A as S₂=60 km/hr.

S - average speed

x - distance between A and B. Total distance, that car travelled = $x+x=2x$ .

$S=\dfrac{2x}{t_1+t_2}=\dfrac{2x}{\dfrac{x}{S_1}+\dfrac{x}{S_2}}=\dfrac{2x}{\dfrac{x(S_1+S_2)}{S_1*S_2}}=$

$=\dfrac{2*S_1*S_2}{S_1+S_2}=\dfrac{2*40*60}{100}=48 \dfrac{km}{hr}$

Answer: average velocity is 0, average speed is 48 km/hr