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In addition to the revision notes for Position v's Time and Distance v's Time Graph on this page, you can also access the following Kinematics learning resources for Position v's Time and Distance v's Time Graph
| Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions | |
|---|---|---|---|---|---|---|
| 3.9 | Position v's Time and Distance v's Time Graph |
In these revision notes for Position v's Time and Distance v's Time Graph, we cover the following key points:
Position vs Time graph consists in two perpendicular axes where Time is shown in the horizontal axis and Position in the vertical one.
The position axis lies both in positive and negative part of coordinate as the position can be also negative but the time axis lies only due positive as no negative time exists.
Position vs Time graph (like all the other motion graphs) does not show the trajectory of the object; it only provides information on how the object moves.
"The gradient of the Position vs Time graph at any point of the graph gives the Instantaneous Velocity".
If the motion is uniform, the instantaneous velocity is the same everywhere; it is the equal to the average velocity.
In non-uniform motion, the position vs time graph is not linear, as the position does not change at the same rate everywhere.
"Steeper the slope (greater the gradient) of a position vs time graph, greater the moving velocity of the object."
In motion with constant acceleration the slope changes at every instant, so we can only calculate the instantaneous velocity through the abovementioned method (the gradient), not the average velocity.
The equation of motion with constant acceleration
or as it is otherwise written,
is quadratic. Its form is
In the actual application of the above equation in Kinematics, we have
From Mathematics, it is known that the graph of a quadratic function is a parabola. When the coefficient A is positive, the arms of the parabola are upwards, and when A is negative, the parabola is arm-down. This means when acceleration is positive, the arms of the parabola are upwards, i.e. the position increases more and more for equal time intervals
The table below clarifies the sign of acceleration in different situations:
| How the object is moving? | Speeding up towards positive | Slowing down towards positive | Speeding up towards negative | Slowing down towards negative |
|---|---|---|---|---|
| What is the sign of acceleration? | Positive | Negative | Negative | Positive |
The Distance vs Time graph is identical to the Position vs Time graph when the object is moving in the positive direction but it is flipped vertically when the object is moving towards negative. This is because distance cannot be negative; it represents the path length followed by an object during its motion. The other difference is that unlike in the Position vs Time graph, the vertical axis of the Distance vs Time graph cannot extend towards the negative direction.
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