The_Engineer said:If a particle undergoes multiple phases of motion (ex. accelerating, then decelerating, then constant acceleration, etc..) then how can you determine where the particle's final position is?
I'm imagining a v-t diagram and if you get the area under all of the velocity curves then you get the total displacement, but not the final position (the particle may have been moving backwards...) How do you get the final position?
Let's keep it simple and apply this only to one dimension.
EDIT: Does integrating the absolute value of all the velocity equations yield total displacement while just integrating yields the final position?
Andrew Mason said:Are we to assume that all motion is in one dimension?
If the particle is moving backwards the velocity will be negative so the change in displacement during that period, ∫vdt, will be negative.
Displacement is the distance from the origin with its direction from the origin (ie. + or - x). The change in displacement is defined as the final displacement (position) minus the initial displacement .
AM
The_Engineer said:Say you have a v-t diagram for the motion of a particle in one dimension where the velocity is positive at first and then negative later. If you integrate and get zero, why doesn't that mean that the particle started moving and then came back to the origin?
Kinematics is the branch of physics that deals with the study of motion and the factors that affect it, such as velocity, acceleration, and displacement.
Speed is a measure of how fast an object is moving, while velocity is a measure of both speed and direction. In other words, velocity takes into account the direction of an object's motion, while speed does not.
Acceleration is calculated by dividing the change in an object's velocity by the time it takes for that change to occur. It is measured in meters per second squared (m/s^2).
Average velocity is the total displacement of an object divided by the total time it took to cover that displacement. Instantaneous velocity, on the other hand, is the velocity of an object at a specific moment in time.
The equation for displacement is: Δx = xf - xi, where Δx is the change in position, xf is the final position, and xi is the initial position.