Answer:
See bolded below.
Explanation:
Consider the " Before " and " After. " " Before, " this particle 1 was trying to catch up with this particle 2, and " after " particle one had collided with particle two. Take a look at the attachment below for a more detailed examination.
Here is how this will play out. Particle 1, with great velocity, will hit particle 2, which would mean that Particle 2 has less velocity than Particle 1. Now after the collision, energy is transferred to Particle 2, and while Particle 1 has now stopped in it's tracks, Particle 2 - with more energy than before - will continue as long as it has to before friction eventually brings it to a stop.
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From this we can conclude that Vf, from the picture below, must have less energy than V1, but more energy than V2 - and vice versa.
The given statements are not true as the only true statement is;
v_f is greater than v₂ but less than v₁.
We are told that two particles are moving to the right named particle 1 and particle 2.
Let the speed of particle 1 be v₁
Let the speed of particle 2 be v₂
Since we are told that Particle 1 catches up with particle 2 and collides with it, it means that Speed of particle 1 is greater than speed of particle 2. Thus;
v₁ > v₂
Now, we are told that the particles stick together after collision and continue with a velocity (v_f).
This means that particle 1 has transferred some of its' kinetic energy to particle 2. This means that the new speed v_f will be lesser than the initial speed v₁ of particle 1 but obviously greater than v₂.
In conclusion, v_f is greater than v₂ but less than v₁.
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