A body travelling along a straight line traversed one thired of the total distance with a velocity ` 4 ms^(-10`. The remaining part of the distance was covered with a velocity ` 2 ms^(-1)` for half the time and with velocity ` 6 ms^(-1)` for the other hald of time . What is the mean velocity averaged over te whle time of motin ?

Explanation

Let (s) be the total distance travelled by body. If ` t_1` is the time taken to over first one thirdd
distance, then ` t_1 = (s//3)/4 = s/ (12) `
Let ` t-2` be the time for each of the remaining two journeys. Then
` (2 s)/3 = 2 t_2 + 6 t_2 = 8 t-2`
or ` t_2 = ( 2 s)/ ( 2 xx 8) = s/( 12)`
Average velocity ` (total distance )/( total time)`
= s/( t-1 + 2 t_2) = s/( 9 s//12) = 2 ( s// 12) = 4 ms^(-1)`.