Two object, each of mass `1.5 kg`, are moving in the same straight line but in opposite directions, The velocity of each object is `2.5 ms^(-1)` before the collision during which they stick together. What will be the velocity of the combined object after collision?

Explanation

Mass of first object, `m_(1)`=1.5 kg
Velocity of first object, `v_(1)=2.5ms^(-1)`
So, Momentum of first object=`m_(1)xxv_(1)`
`=1.5xx2.5`
`=3.75kgms^(-1)`
Mass of second object, `m_(2)`= 1.5 kg
Velocity of second object, `v_(2)=-2.5 ms^(-1)` (In opposite direction)
So, Momentum of second object = `m_(2) xxv_(2)`
`=1.5xx(-2.5)`
`=-3.75kgms^(-1)`
Total momentum= 3.75 + (- 3.75)
before collision =3.75-3.75
`=0 kgms^(-1)`
The mass of combined objects will be `m_(1) + m_(2) = 1.5 kg + 1.5 kg = 3.0 kg`. Now, suppose the velocity of combined objects after collision is v m `s^(-1)` . So,
Total momentum=`(m_(1)+m_(2))xxv`
after collision=`3.0xxv`
Now, according to the principle of conservation of momentum:
Total momentum before collision=Total momentum after collision
So, `0=3.0xxv`
And, `v=0/3.0`
or, `v=0ms^(-1)`
Thus, the velocity of the combined objects after the collision will be zero metres per second which means that the combined objects will come to a stop after the collision.