A body of mass m moving along a straight line covers half the distance with a speed of `2ms^(-1)`. The remaining half of the distance is covered in two equal time intervals with a speed of `3ms^(-1)` and `5ms^(-1)` respectively. The average speed of the particle for the entire journey is

Options

A. `3/8ms^(-1)`
B. `8/3ms^(-1)`
C. `4/3ms^(-1)`
D. `16/3ms^(-1)`

Answer

B

Explanation

Let s be the total distance travelled by the body. Let `t_(1)` be the time taken by the body to travel first half of the distance. Then
`t_(1)=(s/2)/2=s/4`
Let `t_(2)` be the time taken by body for each time interval for the remaining half journey
Therefore `s/2=3t_(2)+5t_(2)=8t_(2)` or `t_(2)=s/16`
Average speed `v_(av)=s/(t_(1)+2t_(2))=s/(s/4+2(s/16))=8/3ms^(-1)`