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Grade 10General Physics

A particle completes half of its journey with uniform velocity 'u'. Then it moves with a uniform velocity 'v' through half the time required to complete the remaining half of the journey with a uniform velocity 'w' through the remaining half of the said time. Determine the average velocity.

Profile image of Navjyot Kalra
12 Years agoGrade 10
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1 Answer

Profile image of Sandeep Pathak
11 Years ago
Assume total distance to be S and total time taken is T. Then time taken to travel first part of journey ist_1 = \frac{S}{2u}
Time remaining for rest of journey is
T-t_1 = T-\frac{S}{2u}
so, total distance traveled in this time is
S_2= \left(T-\frac{S}{2u}\right)\left(\frac{v+w}{2}\right)=\frac{S}{2}
T\left(\frac{v+w}{2}\right)=\frac{S}{2}+\frac{S}{2u}\left(\frac{v+w}{2}\right)=\frac{S}{2}\left(1+\frac{v+w}{2u}\right)\\\Rightarrow\langle v\rangle = \frac{S}{T}=\frac{v+w}{1+\frac{v+w}{2u}}

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