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 Sms' 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 s be the total distance travelled by the body. Let `t_1` be the time taken by the body to travel first has 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))=8/3 ms^(-1)`