Position-time graphs display a constant velocity by a straight, diagonal line. An accelerating object is represented by a curved line on a position-time graph. If the line becomes flatter over time, then the object is slowing down. If the line becomes steeper over time, then the object is speeding up.
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A horizontal ine on a velocity-time graph represents a constant velocity motion. An accelerated motion is represented by a diagonal line on a velocity-time graph. Lines located in the positive region represent objects with a positive velocity and lines in the negative region represent objects with a negative velocity.
 

This question includes the following animation:

You will have to match it to a position-time or a velocity-time graph. Tap on the graph to toggle through the various graph options until you find a matching graph.

Your goal is to find the graph - either position-time or velocity-time - that matches the animation. And so you will first need to be able to describe the motion of the object - speeding up, slowing down, constant speed, etc. Then you will need to understand the graphs well enough to find the one that describes the same type of motion. The following comments will help:

Single Stage vs. Multi-Stage? Six of the animations in this Concept Builder are simple, single-stage motions. The object is moving in the same manner the whole time. Matching a single stage motion to a graph means you need to look for graph with a single line on it. Because there is only one motion stage, there will only be one line - either horizontal, diagonal or curved. Five of the animations in this Concept Builder depict multi-stage motions; the object is moving in different directions or in different ways at varying stages of the motion. Such matching graphs will be more complicated (more than one line) because they must describe more than one motion stage.

Constant Velocity vs. Changing Velocity (Acceleration): Inspect the car's motion (during each stage) to see if it is a constant velocity motion or a changing velocity motion. For a constant velocity motion, the car will move the same distance during every second. It will leave a trail of dots that are equally spaced. A changing velocity motion will have an acceleration. The car will either slow down or speed up; the trail of dots will not have equal spacing between consecutive dots.

Direction of Velocity: Velocity is a vector; and so it has a direction. The direction of the velocity will be in the same diection that the object is moving.

Direction of Acceleration: Acceleration is also a vector, but the rule for its direction is much more complicated. If the car is speeding up, then the direction of the acceleration is the same direction that the car is moving. However, if the car is slowing down, then the direction of the acceleration is opposite of the direction that the car is moving.

Position-Time Graphs: If the line on a position-time graph is straight - i.e., has constant slope - then the object is moving with a constant speed. But if the line curves in such a manner as to become steeper and steeper over the course of time, then the object is speeding up. And if the line curves in such a manner as to become less and less steep over the course of time, then the object is slowing down. The directioni that the line slopes - either upward or downward - indicates whether the velocity is positive (for upward slope) or negative (for downward slope).

Velocity-Time Graphs: On a velocity-time graph, a constant speed motion is a horizontal line. Changing speed motions are represented by diagonal lines. If the diagonal line approaches the time axis (either from above or below), then the motion is a slowing down motion. On the other hand, if the diagonal line gets further and further from the time axis, then the motion is a speeding up motion. On a velocity-time graph, a positive velocity is indicated by a line located in the positive region (above the time axis) and a negative velocity is indicated by a line in the negative region (below the time axis).

Now take these basic suggestions and apply it to the animation and graphs in order to find the matching graph. Take your time and (as is always the need in physics) think logically.

 


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