Question

A cyclist is travelling in a straight road for the first half with speed V1 and for the second half time with speed V2 what is average speed of the cycle

Answer 1

Given :-

Velocity of first half = ${v}_{1}$

Velocity for second half =${v}_{2}$

Time taken for first half = ${t}_{1}$

Time taken for second half =${t}_{2}$

Let the total distance traveled = S

${t}_{1} = \dfrac{s}{2{v}_{1}}$ ----(1)

${t}_{2}= \dfrac{s}{2{v}_{2}}$ ----(2)

T = ${t}_{1} + {t}_{2}$

T = $\dfrac{s}{2{v}_{1}} + \dfrac{s}{2{v}_{2}}$

T = $\dfrac{S({v}_{1}+{v}_{2})}{2{v}_{1}{v}_{2}}$

Now,

${V}_{avg} = \dfrac{S}{T}$

Putting the value of 'T'

${V}_{avg} = \dfrac{S}{\dfrac{S({v}_{1}+{v}_{2})}{2{v}_{1}{v}_{2}}}$

${V}_{avg} = \dfrac{2{v}_{1}{v}_{2}}{{v}_{1}+{v}_{2}}$

Hence, Above given is the average speed of body.