A particle moving in a straight line covers half the distance with a speed of `3 m s^(-1)`. The other half of the distance is covered in two equal time intervals with speeds of `4.5 m s^(-1)`, and `7. 5 m s^(-1)`, respectively. Find the average speed of the particle during this motion.

Options

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))`

Answer

C

Explanation

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))`