Question

A car moves from X to Y with a uniform speed vu and returns to y with a uniform speed vd. The average speed for this round trip is

Answer 1

Karan Gupta

51 Points

Let distance travelled in going from X to Y = x

Hence distance travelled back from Y to X = x

Total Distance = 2x

 

Time for forward trip = x/vu

Time for return trip = x/vd

Hence total time = x/vu + x/vd

 

Average speed = Total distance/Total time = 2x / (x/vu + x/vd) = 2(vu)(vd) / (vu+vd)

Answer 2

Answer:

The average speed for this round trip

$= \frac{2VᵤV₍d₎}{Vᵤ + V₍d₎}$

Explanation:

We know,

$average \: speed = \frac{total \: distance}{total \: time}$

Let t₁ and t₂ times taken by the car to go from x and y and then from y to x, respectively,

$t₁ + t₂ = \frac{xy}{Vᵤ} + \frac{xy}{V₍d₎}$

$t₁ + t₂ = \frac{xy}{Vᵤ} + \frac{xy}{V₍d₎} = xy( \frac{Vᵤ + V₍d₎}{VᵤV₍d₎}$

Total distance travelled = xy + xy = 2xy

So,average speed

$= \frac{2xy}{xy \times \frac{Vᵤ + V₍d₎}{VᵤV₍d₎} } = \frac{2VᵤV₍d₎}{Vᵤ + V₍d₎}$

The average speed for this round trip

$= \frac{2VᵤV₍d₎}{Vᵤ + V₍d₎}$