The figure shown the velocity as a function of the time for an object with mass `10kg` being pushed along a frictioniess horizontal surface sby external horizontal force. At `t=3s`, the force stops pushing and the object moves freely. It then collides head on and sticks to another object of mass `25kg`

Options

A. External force acting on the system is `50N` from `tj=0` to `t=3` sec.
B. Speed of the `2^(nd)` particle just before the collision is `1m//s`.
C. before collison both bodies are moving in the same direction.
D. before collision, bodies are movng in oppostie direction.

Explanation

From graph in time from `t=0` to `t=3` sec.
acceleration of object of mass `m_(1)=10kg` is
`a=(15-0)/(3)=5m//s^(2)`
`therefore` Force on object of mass `m_(1)` from `t=0` to `t=3` sec. (i)
`=10xx5=50N`
Before and after collision at `t=4` sec. the velocites of blocks are as shown.

after collision
`therefore` initial momentum of system
`=m_(1)u_(1)+m_(2)=150+25u_(2)`
final momentum of system
`=(m_(1)+m_(2))v=35xx5=175`
From conservationof momentum
`therefore 150+25u_(2)=175`
or `u_(2)=+1 m//s`
`therefore` speed of second particle just before colision is `1m//s` and before collision both blocks move in same direction.