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A particle moving in a straight line cov...

A particle moving in a straight line covers half the distance with speed `v_(0)`. The other half of the distance is covered in two equal time intervals with speed `v_(1)` and `v_(2)`, respectively. The average speed of the particle during this motion is

A

`(v_(0)(v_(1)+v_(2)))/(v_(0)+v_(1)+v_(2))`

B

`(2v_(0)(v_(1)+v_(2)))/(v_(0)+v_(1)+v_(2))`

C

`(2v_(0)(v_(1)+v_(2)))/(2v_(0)+v_(1)+v_(2))`

D

`(v_(0)(v_(1)+v_(2)))/(2v_(0)+v_(1)+v_(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
A particle …………..

`A to B : (S)/(2) = v_(0)t_(0) implies t_(0) = (S)/(2v_(0))`
`B to D : (S)/(2) v_(1)t +v_(2)t implies t = (s)/(2(v_(1)+v_(2)))`
Average speed `= (s)/(t_(0)+t+t)`
`= (2v_(0) (v_(1)+v_(2)))/(2v_(0)+v_(1)+v_(2))`
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