Motion With Graphs with Examples

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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


examples of position vs time graphs
area under velocity graph example
comparing two velocity time graphs
motion graphs solutions
rotational kinematics graphs acceleration vs time find acceleration
comparing velocity and displacement graph
constant velocity gives what acceleration and force graphs
examples velocity vs time graph projectile motion
velocity vs time graph motion physics formulas
examples of physics velocity time graphs
rotational motion graph examples
acceleration vs displacement graphs
formuales for motion time graph
Constant Motion Graph image
physics motion graphs displacement
projectile motion velocity vs time graph
acceleration velocity graphs car force
how to calculate force given position vs time graph
projectile motion graphs
circuits cheat sheets + power triangle
Example problems on acceleration and velocity graphs
finding area of a graph displacement
projectile motion example graphs
acceleration from force vs time graph
velocity vs time graph examples
acceleration time graph no motion
projectile motion position vs time graph
projectile acceleration and velocity graph
Physics Velocity-time Graphs
find acceleration from displacement graph
distance vs time graph cheat sheet
calculating projectile motion using velocity graphs
how to calculate displacement with a force time graph
acceleration graphs different examples
the area under the force displacement curve gives
acceleration vs time graph illustrate the motion
how to calculate acceleration from a velocity vs distance graph
acceleration time graph for projectile
Finding displacement in a force–displacement graph
distance time graph projectile motion
acceleration vs time graph projectile
calculate impulse "acceleration vs time" graph
comparing motion at a constant velocity
the area of a force displacement graph gives us
example force an motion graph
velocity time graphs for projectile motion
explanation of jump acceleration force time curve
velocity, and acceleration versus time for projectile motion , graphs
"motion-time graph"