NAME: Gabriel-Ohanu Emmanuel
PARTNER: Baptiste Gilman
TITLE: Graph Matching
PURPOSE: The purpose of the experiment was to analyze the motion of a student walking along a straight line in front of the motion detector moving back and forward with different speed trying to match the graph provided. To also understand and interpret graphs of distance vs time and velocity vs time. To also know what the slopes of the each graph represent which tells how far the student travelled, the speed and whether the motion of the student is accelerating or decelerating.
The particle position X is the with respect to a chosen point that is considered as the origin of the coordinate system. The motion of a particle is completely known if the particle’s position in space is known at all times. s. The displacement Dx of a particle is defined as its change in position in some time interval. As the particle moves from an initial position xi to a final position xf , its displacement is given by
Δx = xf - xi
the difference between displacement and distance is important to note. Distance is it length of a path followed by a particle The average speed Vavg of is a scalar quantity defined as the ratio total distance traveled to the total time interval required to travel that distance ≡
The average velocity Vx,avg of a particle is defined as the particle’s displacement Dx divided by the time interval Dt during which that Displacement occurs:
The instantaneous speed of a particle is defined as the magnitude of its instantaneous velocity. As with average speed, instantaneous speed has no direction associated with it.
The instantaneous velocity equals the limiting value of the ratio approaches zero. The instantaneous velocity can be positive, negative, or zero
Remembering that we see that or.
The equation tells us that the position of the particle is given by the sum of its original position at the time t=0, plus the displacement that occurs during the time interval that occurs during the time interval. The time at the beginning of the interval =0 so= and our equation becomes
Particle under constant acceleration αx moving along x axis
(a) position-time graph (b) velocity-time graph (c) acceleration-time graph If the acceleration of a particle varies in time, its motion can be complex and difficult to analyze. A very common and simple type of one-dimensional motion, however, is that in which the acceleration is constant. In such a case, the average acceleration αx,avg over any time interval is numerically equal to the instantaneous acceleration αx at any instant within the interval, and the velocity changes at the same rate through- out the motion. This situation occurs often enough that we identify it as an analysis model: the particle under constant acceleration. In the discussion that follows, we generate several equations that describe the motion of a particle for this model. If we replace αx,avg for αx in equation below and take ti =0 and tf to be any later time t, we find that αx =
αxt (for constant αx) eqn1
This powerful expression enables us to determine an object’s velocity at any time t if we know the object’s initial velocity and its (constant) acceleration αx. A velocity–time graph for this constant-acceleration motion is shown in diagram A. The graph is a straight line, the slope of which is the acceleration αx; the (constant) slope is consistent with αx=d being a constant. Notice that the slope is positive, which indicates a positive acceleration. If the acceleration were...
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