A particle starts from rest and traverses a distance l with uniform acceleration, then moves uniformly over a further distance 2l and finally comes to rest after moving a further distance 3l under uniform retardation. Assuming entire motion to be rectilinear motion the ratio of average speed over the journey to the maximum speed on its ways is

Options

A. `4/5`
B. `3/5`
C. `2/5`
D. `1/5`

Answer

B

Explanation

Let `t_(1) , t_(2) and t_(3)` be the time taken by the particle to cover the distances 2x , 4x and 6x respectively . Let v be the velocity of the particle at B i.e . maximum velocity.

The particle moves with uniform acceleration from A to B .
For motion from A to B,
Average velocity `= (0 +v)/2 = v/2`
Time taken , `t_(1) = (2x) / (v//2) = (4x)/v`
The particle moves with uniform velocity from B to C,
`:. t_(2) = (4x)/v`
The particle moves with uniform retardation from C to D ,
`:. t_(3) = (6x)/((0+v)//2)=(12x)/v`
Total time taken = `=t_1+t_2+t_3=(4x)/v+(4x)/v+(12x)/v=(20x)/v`
`v_(av)=(2x +4x+6x)/(20x//v)=(12v)/20" or " v_(av)/v = 12/20 = 3/5`