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For that period of time, d(t) (the distance) is not changing so the motion is zero velocity.

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Q: When d-t graph is parallel to time axis what can you say about the motion?

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That the object is moving at a constant velocity

time, distance

In a velocity-time graph it will be the time axis (where velocity = 0). On a distance-time graph it will be a line parallel to the time axis: distance = some constant (which may be 0).

distance = speed x time the speed is the slope of the line which if parallel to X axis is zero - that means speed = 0 and distance is not changing with time, so the object is at rest ( not moving) relative to the observer

As the body is at rest, its distance from some point is not changing, so the graph will be a straight line parallel to the time axis (including the possibility of being on the time axis).

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object is at rest

Said object is not moving

constant positive acceleration

If the line is parallel to the time axis, this means that the distance is not changing, so the object is not moving.

That the object is moving at a constant velocity

The graph is parallel to the time axis, normally the horizontal axis.

A position-time graph, is one in which position is plotted on the y-axis and the time is on the x-axis. A position-time graph is similar to a distance-time graph, but direction of motion in the y-axis.

You can't. Such a graph is only appropriate for motion in a single dimension.

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.

time, distance

If the graph if speed vs. time is a straight line parallel to the time axis, then the speed is not changing.Acceleration is the slope of the line on such a graph. Slope is (speed change) divided by (time for the change).Since the speed doesn't change over any period of time, the slope of the line is zero.The object's speed is constant. Its acceleration is zero.

In a velocity-time graph it will be the time axis (where velocity = 0). On a distance-time graph it will be a line parallel to the time axis: distance = some constant (which may be 0).