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Position vs. Time Graphs:

  1. Graphs are commonly used in physics. They give us much information about the concepts and we can infer many things. Let’s talk about this position vs. time graph. As you see on the graph, X axis shows us time and Y axis shows position. We observe that position time graphposition is linearly increasing in positive direction with the time. We understand from this linear increasing, our velocity is constant. If it was not constant we would see a curved line in our graph. Now, we use this graph and make some calculations.

From the given graph we calculate velocity; there is another way of this calculation. We just look at the slope of the graph and find the velocity. What we mean by slope is;

which is the equation we use in calculation of the velocity.

2. Position is increasing positive direction.

position time graph In this graph our velocity is changing. As a result of this change graph has curved line not linear. So position does not increase linearly. We can also find the velocity of the object from this graph. We should first find the slope of the curve and calculate the velocity.



Example Using the given graph find the velocity of the object in intervals (1s – 3s) and (3s – 5s).

position time graph example


In graph problems you should be careful while reading it. For example, in this example in the interval (3s-5s) position does not change. You can easily see it from the graph, but I want to show the calculation of this and it gives us same result. If there is no change in position then there is no velocity or vice versa. You can say more things about the motion of the object by just looking of the graph. The important thing is that you must know the relations, meaning of the slopes or area of the graphs. We will solve more examples using graph for deep understanding and analyzing the motion from the graphs.

3. This position time graph is an example of increasing position in negative direction. Red line shows nonlinear increasing and black line shows linear increasing. We say that linear increasing in position is the result of constant velocity which means zero acceleration. Moreover, nonlinear increase in the position is the result of changing velocity and it shows there is a nonzero acceleration.

position time graph negative direction






4. Until now we saw graphics including speeding up motion in positive and negative directions. Now we talk about a little bit increasing position time graph slowing down object’s graphs. For example, in this given graph, our position is decreasing in different directions. Red line shows the position of the object which is slowing down in negative direction and black line shows the position of the object slowing down in positive direction. However, the blue and green lines show the linear decrease in position in positive and negative directions.





We have seen various type of position vs. time graphs. I think they will help you in solving problems. It is really easy, you should just keep in mind that “slope shows the velocity”.


Velocity vs. Time Graphs

In velocity vs. time graphs, x axis is time as in the case of position vs. time graphs and y axis is velocity. We can benefit from this graph by two ways. One of them is area under the graph which gives the displacement and the slope which gives the acceleration.

1. We have talked about different kinds of motion such as, constant motion having constant velocity, accelerated motion like speeding up or slowing down. For instance, in this graph as it seen our velocity is constant, time passes but velocity does not change. What you see when you look at this graph?

velocity time graph


We see the relation of velocity and time, how velocity is changing with time. It can be said for this graph acceleration is zero because there is no change in velocity. Moreover, from velocity vs. time graphs we can calculate displacement of the object. How can we do this? Let’s think together. First, look at the definition of displacement;

Since, the velocity times time gives us displacement the area under the velocity vs. time graph also gives us the displacement of the object. Look at the example given below to understand what we mean by the area under the graph.

Example Using the given graph calculate the displacement of the object for the interval (0s – 4s).

velocity time example

To solve this problem, I use the technique given above and classic formula. The area under the graph will give us the displacement. Then we

compare the results of two techniques.

velocity time graph example solution

As you can see, the results are the same, thus, we can say that in velocity vs. time graphs we can find the displacement by looking at the area under the graph.






2. In this graph there is a linear increase in velocity with respect to time so, the acceleration of the motion is constant. Moreover, we can also calculate the displacement by looking at under the area of the graph. Let’s solve another example for deep understanding.


velocity vs. time graph










Example Calculate the displacement of the car from the given graph.

velocity vs. time graph example



We can calculate displacement by using the area under the graph, to do this we can first calculate the area of the triangle shown with blue lines and then rectangle shown with red lines. Finally the sum of these two areas gives us the total displacement of the car.

velocity vs. time graph example solution


3. This graph shows the different accelerated motions. The lines are curved because acceleration is not constant. They represent the decreasing and increasing velocity in positive and negative directions. However, we do not deal with such problems now.

velocity vs time graph










We have discussed the velocity vs. time graphs. When you look at these graphs you can find the displacement and acceleration of the object by looking at the slope for acceleration and area for displacement.



Kinematics Exams


calculating displacement on position-time graph
Describing Motion with Velocity vs Time Graphs
example of motion story physics(graph)
when can we say that the graph is decreasing
is displacement used to graph position vs time graphs?
displacement-time graph of slowing down
relating graphs to stories increasing decreasing
distance graph determine
decreasing graph story
motion graph stories
what does a distance vs time graph look like for decreasing
describing displacement time graphs
Relating Graphs to Stories
increasing graph stories with time
motion stories to graph
speed graphs stories
examples of graphs relating to stories
slow increasing nonlinear graph
curved line graph stories
motion graph slowing down
velocity vs time story graph
how does a graph look when velocity is increasing, decreasing
graph the motion story
motion graph from story
line graph where there is a curved increase
displacement distance graph what happens as you increase speed
"story graph" slope
physics increasing decreasing constant graphs
time distance graph stories
slow fall calculate acceleration on a graph
line graph stories
decreasing and increasing speed physics
non linear graphs stories
how will acceleration versus distance curve look like for a free fall
how do you find if an interval is decreasing or increasing just by looking at the graph
velocity time graph stories
distance - time, displacement-time graphs comparison
distance and velocity story graphs
what happens when we change the position of a triangle on a graph
tell me a story motion physcis
how a graph can be used in describing motion
physics graphing stories
what happens when we change position of triangle on graph
when is motion slow on a graph
motion in curve and slope camprision
how to read increasing and decreasing graphs physics
"tell me a story"+graphs
when do we say that an object is in motion?
icreasing decreasing curve v-t graph
physics stories with problems that use graph