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

Answer

B

Explanation

Let 2S 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.
`:.t_(1)=S/2 `
Let `t_(2)` be the time taken by the body for each time interval for the remaining half journey.
`:.S=3t_(2)+5t_(2)` or` t_(2)=S//8`
Average speed `=("Total distance travelled")/("Total time taken")`
`=(2S)/(t_(1)+2t_(2))=(2S)/(S/2+(S/8))=(2S)/(S/2+S/4)=8/3ms^(-1)`