Velocity-time and Position-time Graphs

The velocity of an object is the rate of change of position of any particle with respect to a frame of reference. Velocity is a function of time. Velocity-time graph is representation of variation of velocity of any moving object with respect to time. Velocity-time graphs are also called speed-time graphs. The vertical axis of a velocity-time graph represents  the velocity of the object. The horizontal axis represents the time from the start of motion.

The motion of an object over a period of time is described by a position-time graph. The position of a particle in metres is represented on the y-axis and time in seconds is plotted on the x-axis.

There are three types of kinematics graphs-

• Position-time kinematics graph

• Velocity-time kinematics graph

• Acceleration-time kinematics graph

velocity time graph

Acceleration is shown by the slope of the velocity-time graph. The acceleration is zero if the velocity-time graph has a horizontal slope. This signifies that the thing is either stationary or travelling at a consistent pace. When the slope is rising, the rate of acceleration rises. Acceleration decreases if the slope is negative.

The information about the journey taken by an object is given by velocity-time graphs.

In velocity-time graph – 

On y axis velocity is plotted

On x axis the time is plotted 

The distance travelled by the object and the acceleration of an object can also be calculated by A velocity-time graph.

Imagine a situation that on a straight track the sprinter is just taking off from the starting blocks for running a short race. For the starting first few seconds of the race, the sprinter will pick up more speed as she starts with a burst of speed. After that she keeps running at her top speed until he finishes the race by crossing the finishing line. After that she will slow down. Acceleration is defined as change in velocity. In this case though her direction stays the same but her speed is changing so it means she has an acceleration as velocity is a measure of both direction and speed.

A velocity-time graph can represent the changing in velocity not of the sprinter but for all the other moving objects(any kind of object). In a figure given below , a velocity-time graph of the sprinter is shown how its velocity changes over time. The magnitude of velocity of the sprinter first increases for the first 4 seconds, after that it remains constant for the next 3 seconds and finally it decreases for the last  3 seconds after she crosses the finish line.

The slope of the Velocity-Time Graph

It is possible to determine the acceleration of an item by examining the slope of a velocity-time graph. If the slope of the velocity-time graph is a horizontal line, then the acceleration is equal to zero. This indicates that the item is either at rest or is travelling at a constant speed, without increasing or decreasing its speed as it approaches. If the slope is positive, the acceleration is rising in magnitude. If the slope is negative, this indicates that the rate of acceleration is declining.

2. Position-Time Graphs

The position-time graph tells you at what time where an object is located. The slope of the graph will  tell you about the speed of the object. 

It is a graph where instantaneous position x of a particle is plotted on the y-axis and the time t on the x-axis as shown below in the figure:

Position time graph for uniform motion

• In  uniform motion objects cover equal distance in equal intervals of time.

• For uniform rectilinear motion the x-t graph is a straight line inclined to the time axis.

Noticeable things about the slope of the position time graph.

• instantaneous velocity Is given by The slope of the tangent drawn at any point to the x-t curve.

• Steeper is the slope at any point, more is the speed at that point.

• Speed is given by the The numerical value of the slope of the tangent drawn to the x-t curve.

• We can find at which particular instant the direction of motion of the particle is changing, these points are where the slope of x−t plot is zero 

• speed would be maximum at The instant where the tangent is drawn to the x-t plot is steepest. So from the x-t graph we can also get knowledge of speed.

3. Area under velocity-time and position-time graphs

The area under a velocity-time graph gives the value of displacement. For objects moving in backward direction velocity can be negative. The displacement can also be negative. An area below  the x-axis has a negative value. Positive value is given by the  area above the  x-axis. While calculating the total displacement, we should add  displacements including their plus(+) and minus(−) signs. This is a common error made by students. 

The area under the position time graph gives nothing.

Conclusion :

• Slope of the velocity time graph gives acceleration.

• Slope of the position time graph gives velocity.

• Area under the velocity time graph gives displacement.

Area under the position time graph gives nothing.