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

Options

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

Answer

B

Explanation

Let (S) be the total distance travelled by the body. Let ` t-1` be the tiem taken by the body to travel first half of the distance (i.e. S//2) . Then
` t_1 = (S//2)/2 = S/4`
Let t_2` be the time tanen by body for each tiem interval for the remaining half journey . Therefore,
:. (S//2) = 3 t_2 + t-2 = t-2 ` or ` t_2 = (S//16)`
Average speed,
` v_(av) = S/(t-1 + 2 t_2) = S/((S//4) + 2 (S/16)) = 8/3 ms^(-1)`.