A particle travels along a straight line. It covers halg the distance with a speed (v). The remaining part of the distance was covere with speed `v_(1)` for half the time and with speed `v_(2)` for the other half the time . Find the average speed of the particle over the entire motion.

Explanation

If s is the total distance travelled by the particle, then
`(s)/(2)=v_(0)t_(1) rArr t_(1)=(s)/(2v_(0))`
If t is the time taken by particle to travel remaining distance s/2, then
`(s)/(2)=(v_(1)t)/(2)+(v_(2)t)/(2)=(v_(1)+v_(2))(t)/(2)` or `t=(s)/((v_(1)+v_(2)))`
Average speed `=(s)/(t_(1)+t)=(s)/((s)/(2v_(0))+(s)/((v_(1)+v_(2))))=(2v_(0)(v_(1)+v_(2)))/(v_(1)+v_(2)+2v_(0))`