Kinematics Vel-time graph

A position versus time graph for a free-falling object is shown below.  the small initial slope indicates a small initial velocity and the large final slope indicates a large final velocity. Finally, the negative slope of the line indicates a negative (i.e., downward) velocity. A velocity versus time graph for a free-falling object is shown below. the velocity-time graph reveals that the object starts with a zero velocity (as read from the graph) and finishes with a large, negative velocity; that is, the object is moving in the negative direction and speeding up. An object that is moving in the negative direction and speeding up is said to have a negative acceleration This analysis of the slope on the graph is consistent with the motion of a free-falling object - an object moving with a constant acceleration of 9.8 m/s/s in the downward direction. Positive VelocityZero Acceleration Positive VelocityPositive Acceleration The Importance of Slope The shapes of the velocity vs. time graphs for these two basic types of motion - constant velocity motion and accelerated motion (i.e., changing velocity) - reveal an important principle. The principle is that the slope of the line on a velocity-time graph reveals useful information about the acceleration of the object. If the acceleration is zero, then the slope is zero (i.e., a horizontal line). If the acceleration is positive, then the slope is positive (i.e., an upward sloping line). If the acceleration is negative, then the slope is negative (i.e., a downward sloping line). This very principle can be extended to any conceivable motion. Since the graph is a velocity-time graph, the velocity would be positive whenever the line lies in the positive region (above the x-axis) of the graph. Similarly, the velocity would be negative whenever the line lies in the negative region (below the x-axis) of the graph. As learned inLesson 1, a positive velocity means the object is moving in the positive direction; and a negative velocity means the object is moving in the negative direction. So one knows an object is moving in the positive direction if the line is located in the positive region of the graph (whether it is sloping up or sloping down). And one knows that an object is moving in the negative direction if the line is located in the negative region of the graph (whether it is sloping up or sloping down). And finally, if a line crosses over the x-axis from the positive region to the negative region of the graph (or vice versa), then the object has changed directions. Now how can one tell if the object is speeding up or slowing down? Speeding up means that the magnitude (or numerical value) of the velocity is getting large. For instance, an object with a velocity changing from +3 m/s to + 9 m/s is speeding up. Similarly, an object with a velocity changing from -3 m/s to -9 m/s is also speeding up. In each case, the magnitude of the velocity (the number itself, not the sign or direction) is increasing; the speed is getting bigger. Given this fact, one would believe that an object is speeding up if the line on a velocity-time graph is changing from near the 0-velocity point to a location further away from the 0-velocity point. That is, if the line is getting further away from the x-axis (the 0-velocity point), then the object is speeding up. And conversely, if the line is approaching the x-axis, then the object is slowing down. Q1. Consider the graph at the right. The object whose motion is represented by this graph is ... (include all that are true): moving in the positive direction. moving with a constant velocity. moving with a negative velocity. slowing down. changing directions. speeding up. moving with a positive acceleration. moving with a constant acceleration. Q2. The velocity-time graph for a two-stage rocket is shown below. Use the graph and your understanding of slope calculations to determine the acceleration of the rocket during the listed time intervals. When finished, click the buttons to see the answers. (Help with Slope Calculations) t = 0 - 1 second t = 1 - 4 second t = 4 - 12 second Answers:A1: a, d and h apply. a: TRUE since the line is in the positive region of the graph. b. FALSE since there is an acceleration (i.e., a changing velocity). c. FALSE since a negative velocity would be a line in the negative region (i.e., below the horizontal axis). d. TRUE since the line is approaching the 0-velocity level (the x-axis). e. FALSE since the line never crosses the axis. f. FALSE since the line is not moving away from x-axis. g. FALSE since the line has a negative or downward slope. h. TRUE since the line is straight (i.e, has a constant slope). A2: a.40ms2 b: 20 ms2 c: -20 ms2 Observe the motion of the two-stage rocket and the corresponding velocity-time graph below. The rocket has two consecutive fuel stages followed by a free-fall motion (no fuel). In the two fuel stages, the rocket experiences an upward acceleration of +10 m/s/s and +4.29 m/s/s respectively. This acceleration is depicted by the slope on the velocity-time graph. After ten seconds, the second fuel stage ends and the rocket is acted upon only by the force of gravity. It subsequently experiences a downward acceleration of -10 m/s/s. Note however, that from 10 to 16 seconds, the rocket continues moving upward (the velocity values are positive). During these six seconds, the rocket is moving upward but slowing down (the acceleration is downwards or negative as denoted by the negatively sloped line). It is not until after t =16 seconds that the rocket begins to move downwards The Big Misconception "doesn't a more massive object accelerate at a greater rate than a less massive object?" "Wouldn't an elephant free-fall faster than a mouse?"  Free-fall is the motion of objects that move under the sole influence of gravity; free-falling objects do not encounter air resistance. More massive objects will only fall faster if there is an appreciable amount of air resistance present. Kinematics-Velocity time - M. Abdul Mumeed. +966507433412 1 © Md. Abdul Mumeed, Senior Secondary Teacher in PHYSICS at I. I. School, Riyadh, K.S.A.