:Troll:
The slope of a line on a position vs. time graph would represent the a velocity of the object being described.
If you have an object that is accelerating, then a position vs. time graph will give you a parabola which is pretty but is very hard to measure anything on - especially hard to measure the acceleration (or the curve of the line). If however, you graph position vs. time squared, you get a nice straight line (if you have constant acceleration) and therefore, you can measure the slope and get the acceleration. Remember: x = 1/2at2 so if you graph x vs. t2 then the slope = 1/2 a or a = 2*slope No matter what you are measuring, you always want to graph a straight line. hope that helps
The dependent variable.
The gradient of the graph.
:Troll:
The slope of a line on a position vs. time graph would represent the a velocity of the object being described.
The position.
Position-Time GraphYou can graph motion on a position vs time graph. On a position vs time graph, position is on the y-axis and time is on the x-axis. If the velocity is constant, the graph will be a straight line and the slope is average velocity. If the motion is accelerating, the graph will be a curved line.Velocity-Time GraphYou can also graph motion on a Velocity-Time graph. On a velocity vs time graph, velocity is on the y-axis, time is on the x-axis. If the graph is a straight line, velocity is constant and the slope is average acceleration. Also, on a velocity vs time graph, the area under the line is displacement.Refer to the related link for illustrations of the different graphs of motion and their meanings.
Your acceleration vs. Time graph is the slope of your velocity vs. time graph
Speed. More specifically... velocity.
magnitude of acceleration at every point on the graph
The slope of a position/time graph is the speed (magnitude of velocity).If the graph's slope is changing, that means the speed is changing, andthat would be accelerated motion.
postion is the area under the slope
If the position is graphed vs time, then the slope (rate of change of position with respect to time) will be the same (parallel).
If a position versus time graph is parabolic, then:Speed versus time is a straight line.Acceleration (magnitude) vs time is a horizontal line, so the acceleration is constant.The graph of height/time for a stone or a baseballtossed upward is an inverted parabola.
Position time graph is useful only in the case of 1D motion, you can't made a x-t graph for 3D motion (try ;) ). You need extra efforts to do this because you need a time refrence. So position time graph is valuable for straight line (sometimes 2D) motion only, not for 3D.