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Motion Graphs

Motion graphs are used to characterized constant acceleration motion. Graphs and charts are very useful because they are used for communicating information in visual form. These are used in all fields like in newspapers, businesses, magazines, to show the economic data, annual reports, profits and loss, even used in maths and all other branch of science like chemistry and physics to show the variations and relation between two variables.

When some complicated information are seemed to problematic and require an illustration then graph is the best idea to represent them. It shows all points quickly and visually. This is a source which is used in coordinate system of maths and easily visualizes a function and also useful for calculations based on the functions. This is a representation of objects which are link to one another. These objects are shown on two vertices one is $x$ and other is $y$-axis. 

Here we are discussing about the topic which are used to represent the motion of object. It can be of various types like the graph between distance and time which shows the variation in distance with time, speed and time graph, graph for projectile motion or Simple Harmonic Motion etc.

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Linear Motion Graphs

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Linear graphs are made between the varying quantity with respect to the time.
Varying quantity whose graphs are made with respect to time could be distance, velocity, acceleration.

Generally, motion of the object along the straight line is considered :

Examples are:

a)
Distance - Time Graph (S-T Graph)

b) Speed - Time Graph (V-T Graph) (Graphing Speed)

c) Acceleration - Time Graph (A-T Graph)


In order to understand the concept, first we will understand the main concepts of Kinematics which are used to make these graphs. These concepts are explained below.
Distance : Distance has been defined as the actual path covered during the motion of an object. It does not have any shortcuts. It is measured in m and falls in scalar quantity category.

For example, a girl walks from school to her home and covers 700 meters, so, the distance is 700 meters. The symbol used for distance throughout the unit is ‘s’ i.e. S = 700 m.
Displacement : Displacement is the shortest distance between the point of origin and the point of termination. Thus, displacement concerns or emphasizes on direction and as well as on magnitude. It is a VECTOR quantity and “meter” is its SI unit.Speed : The speed of an object is the ratio of the total distance traveled to the time interval. In Automobiles speeds are measured in miles per hour (mph) or kilometers per hour(km/h). The metric unit of speed is meters per second or (m/s). Speed falls in scalar quantity.
The speed of a vehicle is measured by using a device called speedometer. A vehicle's speedometer is related to the rotation of a gear in the transmission of the car.
Velocity : The Velocity of an object is the speed of an object in a specific direction. It falls in vector quantity. In other words it is the displacement per unit time.

And mathematically Average Velocity = $\frac{(d_{2}-d_{1})}{(t_{2}-t_{1})}$.

where, (d2 – d1) is the displacement that took place in time (t2- t1).
Acceleration : When the velocity of an object changes with time, the object is said to be Accelerating.

For example, the velocity of a bike increases when you Accelerate the bike and decreases when you apply the brakes.

Distance-Time Graph

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The graph of distance is plotted with respect to the time. Generally, time is plotted on the x axis and distance is taken on the y axis of the coordinate system.

Distance-Time Graphs

In the above picture as the time increases the distance remains constant, it represents the object is at rest.

Time is Increasing to right and the distance is increasing constantly with time. The object moves at a constant speed.it is shown by a straight line on a graph.

The curving line indicates the increase in speed, so the line gets steeper.

Distance-Time Graph

• A distance-time graph tells us how far the object moved with time.

• The steeper the graph, the faster the motion.

• A horizontal line means the object is not changing its position that means it is not moving.

• A downward sloping line means the object is returning to its initial position. 

Speed-Time Graph

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Speed-Time Graphs

In the above speed time graph or the velocity time graphs, speed or velocity of the object is generally plotted on the y direction and the time is plotted in the x direction. 

In the graph, a Horizontal line denotes that speed is constant and is not changing over time. Here the object is moving with constant speed.
The steepness in the graph shows the increasing speed which means the object is accelerating.
The third picture denotes the decreasing speed which means the object is decelerating.

Speed-Time Graph

Acceleration-Time Graph

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Acceleration-Time Graphs

In the acceleration time graph, acceleration of the object is generally plotted on the y direction and the time is plotted in the x direction.


Acceleration-Time Graph

Interpreting (Acceleration - Time Graph (A-T Graph))


In the figure, it is explained that how the acceleration time graph can be obtained from the Velocity time graph. At any point in the velocity time graph acceleration at that point can be defined as the slope at that point. 
Positive value of the acceleration in the acceleration time graph shows that velocity in increasing and it is increasing in the positive direction. 

Negative value of the acceleration shows that the velocity is decreasing and it is decreasing in the negative direction. Acceleration goes zero when the slope in the velocity time graph becomes zero. The slope in the velocity time graph becomes zero when the velocity becomes maximum and reaches at its peak point.
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