Position- time graph

Measuring the motion of objects, from a ball to a steam train, is an important component of physics. Plotting an object’s position, velocity, acceleration, and other relevant data is part of this. The graphs of one type of motion can lead to graphs of other types of motion. The velocity-time graph, for example, is derived from the position-time graph. Similarly, the velocity-time graph yields the acceleration-time graph. Each graph’s slopes correspond to different graphical representations of motion.

Let’s discuss the position-time graph for uniform motion!

Position time graph for uniform motion

As we all know, if a body travels the same distance in the same amount of time, we say that it is moving with uniform velocity, and this kind of motion is called uniform motion. Uniform motion is defined as a motion in which the velocity of the moving item remains constant.

Because the body’s velocity remains constant and the body covers the same distance in the same amount of time, this graph depicts the body in uniform motion.

A straight line parallel to the time (t) axis forms this velocity vs. time (v – t) graph.

As a result, option A is true, indicating that the velocity-time graph is a straight line parallel to the time axis.

Its position-time graph is a straight line with the time axis angled up.

The position-time graph

The position-time graph depicts an object’s movement over some time. The x-axis is traditionally used to represent time in seconds, whereas the y-axis is used to plot the object’s position in metres. The position-time graph’s slope offers essential information about the object’s velocity.

Depending on the frame of reference, an object’s position can be positive or negative. The coordinate plane must match whatever the diagram depicts.

Example of position-time graph

Consider a child who is riding her bike on a straight route east and then west. The positive direction is east, and the negative direction is west.

She moved at a consistent rate to the east for the first five seconds of her trip (from t = 0 to t = 5). The straight, ascending line in the positive quadrant of the position-time graph indicates this. Another way of looking at it is that her standing is improving.

She took a rest for the next three seconds (t = 5 to t = 8). A steady horizontal line fixed at +10 m indicates that her position does not move during this period.

Finally, as she nears the end of her ride (t = 8 to t = 15), the girl on the bike begins to accelerate back westward. This is illustrated by a non-constant (curved) line that leads into the graph’s negative quadrant. The negative slope of the line grows over time, indicating that her speed is increasing as she covers more ground each second.

It’s worth noting that when she crosses the x-axis, she’ll have passed through the location where she began.

The slope of the position-time graph

The sort of velocity an object experiences throughout its motion is shown by the slope of a position-time graph. A position-time graph with a constant slope shows a constant velocity. A changing velocity is indicated by a changing slope of a position-time graph. The sign of the velocity is determined by the direction of the slope of the position-time graph. The velocity is negative if it slopes downward from left to right, for example.

The velocity-time graph

The velocity-time graph of an object shows how fast it is travelling at any particular time, as well as whether it is slowing or speeding up. The x-axis is commonly used to depict time in seconds, whereas the y-axis is used to plot velocity in metres per second. A straight-line velocity-time graph depicts objects moving at a consistent rate. The velocity graphs of objects travelling at different speeds are sloping and linear.

Position-time graphs directly lead to velocity-time graphs: the slope of a position-time line indicates the object’s velocity over the same time frame. This makes sense because position vs. time is simply another way of describing metres per second, which is how velocity is defined.

The only difference in this situation is what goes on the y-axis.

Imagine the same girl who was riding her bike in the previous section. She covered 10 metres in five seconds, or 2 metres per second, during the first five seconds of her ride.

Find 2 m/s on the y-axis and draw a smooth line for the first five seconds to graph her velocity in the same time frame. Because her velocity remained constant, the slope on this graph is zero.

The slope of the velocity-time graph

The slope of a velocity-time graph displays an object’s acceleration. The acceleration is zero if the slope of the velocity-time graph is a horizontal line. This indicates that the object is either stationary or travelling at a steady speed with no acceleration or deceleration. The acceleration increases if the slope is positive. Acceleration decreases if the slope is negative.

Conclusion

In kinematics, position-time graphs are the most basic type of graph, allowing us to describe the motion of objects. The vertical axis in these graphs reflects the object’s position, while the horizontal axis represents the amount of time that has passed: the dependent variable, position, is dependent on the independent variable, time. The graph then shows us where the particle can be found after a certain time has passed. Graphs like these assist us in visualising the path of items.