Hey guys, i just have a quick question; many application to the physical world questions have a question where they basically say "describe the movement of the particle". I was just wondering how you interpret the displacement, velocity and acceleration to describe its motion? Like if one is positive and another is negative, or if all are negative or all are positive, and combinations like that. Also what is a limiting position
Thanks heaps!!
You need to understand what motion actually is in the context of our course.
When we talk about motion, we are talking about motion on a straight line. We define a point called the origin (at x=0) and the particle either moves to the left of it, or to the right of it. We define positive displacement as the particle being to the right of the origin, and negative displacement being to the left of the origin. The value of x tells us basically how much to the right/left it is.
What do you mean by combinations? Just analyse each particle separately if you have two or more of them. Don't juggle multiple things at once without reason.
You should well know that velocity describes the rate of change in the displacement. But because we defined positive as right and negative as left, if a velocity is positive it is moving towards the right. Conversely, if it is negative, the particle moves towards the left. v=0 is described as "at rest" because the particle doesn't move.
You should also well know that acceleration describes the rate of change in the velocity. This tells us whether the particle is speeding up or not. If a=0 then the particle is moving at constant velocity (or constantly at rest, if a=0 and v=0 simultaneously). If a is positive, the particle is trying to accelerate to the right, whereas if a is 0, the particle is trying to accelerate to the left.
E.g. x=0, v=2, a=-5: Particle at the origin, moving to the right at 2ms
-1 however accelerating back towards the left at 5ms
-2When they ask about a
limiting position, however, they are talking about what happens to the particle
as time goes to infinity. If you got something like x=e
-t+1, then clearly as t approaches infinity, e
-t approaches 0. So the limiting position is x=1
You should have seen something similar with limiting velocity in the context of the 4U course