By https://physicsassistion.blogspot.com
We can also find the x-velocity of a particle from the graph of its position as
a function of time. Suppose we want to find the x-velocity of the dragster in
Fig. 2.1 at point As point in Fig. 2.1 approaches point point in the
x-t graphs of Figs. 2.7a and 2.7b approaches point and the average x-velocity
is calculated over shorter time intervals In the limit that shown in
Fig. 2.7c, the slope of the line equals the slope of the line tangent to the
curve at point Thus, on a graph of position as a function of time for straight line motion, the instantaneous x-velocity at any point is equal to the slope of the
tangent to the curve at that point.
If the tangent to the x-t curve slopes upward to the right, as in Fig. 2.7c, then
its slope is positive, the x-velocity is positive, and the motion is in the positive
x-direction. If the tangent slopes downward to the right, the slope of the x-t graph
Using an x-t graph to go from (a), (b) average x-velocity to (c) instantaneous x-velocity In (c) we find the slope of the tangent
to the x-t curve by dividing any vertical interval (with distance units) along the tangent by the corresponding horizontal interval (with
time units)
(a) The x-t graph of the motion of a particular particle. The slope of the tangent at any point equals the velocity at that point.
(b) A motion diagram showing the position and velocity of the particle at each of the times labeled on the x-t graph.
and the x-velocity are negative, and the motion is in the negative x-direction.
When the tangent is horizontal, the slope and the x-velocity are zero. Figure 2.8
illustrates these three possibilities.
Figure 2.8 actually depicts the motion of a particle in two ways: as (a) an x-t
graph and (b) a motion diagram that shows the particle’s position at various
instants (like frames from a video of the particle’s motion) as well as arrows to
represent the particle’s velocity at each instant. We will use both x-t graphs and
motion diagrams in this chapter to help you understand motion. You will find it
worth your while to draw both an x-t graph and a motion diagram as part of solving any problem involving motion.
No comments:
Post a Comment