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A particle covers first half of its distance with speed v1 and the rest half in 2 equal intervals of time with speeds v2 and v3.Find the average velocity.

A particle covers first half of its distance with speed v1 and the rest half in 2 equal intervals of time with speeds v2 and v3.Find the average velocity.
 

Grade:9

2 Answers

Arnav Prasad
44 Points
8 years ago
The simplest you must remember should be, average velocity equals to (overall displacement after total time T) / (Total time T).
 
Let total distance be D.
First D/2 covered by V1.
Time taken = D/(2V1) = T1.
 
And the rest...
D/2 = V2T2 + V3T3.
T2 = T3 = T (say).
D/(2T) = V2 + V3.
2T = D / (V2 + V3).
 
Average velocity = D / (T1 + T) = D / (D/2V1 + D/(V2 + V3)) = [(V2 + V3)(2V1) / (2V1 + V2 + V3)].
Arnav Prasad
44 Points
8 years ago
CORRECTIONS MADE.
 
 
 
The simplest thing you must remember should be, average velocity equals to (overall displacement after total time T) / (Total time T).
 
Let total distance be D.
First D/2 covered by V1.
Time taken = D/(2V1) = T1.
 
And the rest...
D/2 = V2T2 + V3T3.
T2 = T3 = T (say).
D/(2T) = V2 + V3.
2T = D / (V2 + V3).
 
Average velocity = D / (T1 + 2T) = D / (D/2V1 + D/(V2 + V3)) = [(V2 + V3)(2V1) / (2V1 + V2 + V3)].

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