An auto travels the first half time with a uniform speed u and the next half tim

Question

An auto travels the first half time with a uniform speed

u

and the next half time with a uniform speed

v

. Find its average speed.

Options:

A . u+v2

B . uv2

C . 2uv

D . uv

Answer: Option A
:
A

Given, speed of the auto during the first half of the journey is

u

and the next half of the journey is

v

Let total time taken for the journey be

T

∴

Time taken for the first half of the journey be

\frac{T}{2}

and the next half of the journey be

\frac{T}{2}

Let the average speed be

V_{a v}

We know,

s p e e d = \frac{D i s t a n c e}{t i m e}

∴

D i s t a n c e = s p e e d \times t i m e

During the first half of the journey, distance,

d_{1} = u \times \frac{T}{2}

During the second half of the journey, distance,

d_{2} = v \times \frac{T}{2}

Total distance

= d = d_{1} + d_{2}

= u \times

\frac{T}{2} + v \times \frac{T}{2}

\Rightarrow d = \frac{T}{2} (u + v)

Average speed,

V_{a v}

\frac{T o t a l d i s t a n c e}{T o t a l t i m e t a k e n}

= \frac{d}{T}

= \frac{\frac{T}{2} (u + v)}{T}

= \frac{u + v}{2}

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