Graphical Representation of Motion

Graphs are used to represent the motion of an object. Graphs provide a convenient method to present basic information about a variety of events.

Examples:

(i) In the telecast of a one-day cricket match.

(ii) Vertical bar graphs show the run rate of a team in each over.

(iii) As you have studied in mathematics, a straight line graph helps in solving a linear equation having two variables.

Uses of graphs: 

(i) Graphs are very useful for comparing the motion of two moving bodies.

(ii) The position of the body at any instant of time can be determined from the distance – time graph.

(iii) Slope of velocity time graph gives the acceleration of an object.

(iv) Straight line graphs help in solving a linear equation in two variables.

(v) Distance time graph tell when and where one body crosses the other body. 

To describe the motion of an object, There is one physical quantity, such as distance or velocity, on another quantity, such as time.

There are two conditions to representing motion.

1. The change in the position of an object with time can be represented on the distance-time graphs. 

2. The variation in velocity with time for an object moving in a straight line can be represented by a velocity-time graphs.

1. Distance-time graphs:

In this graph: 

• Time is taken along the x–axis and distance is taken along the y-axis. 
• Distance-time graphs can be employed under various conditions where objects move with uniform speed, non-uniform speed, remain at rest etc.

Main concept: 

The distance travelled by the object is directly proportional to time taken.

There are two types of graphs: 

(I) Distance-Time Graphs for Uniform speed. 

(II) Distance-Time Graphs for Non-uniform speed. 

Distance-Time Graphs for Uniform speed: 

Gradient: Slope of the graph.

Horizontal section of graph indicate periods of rest. 

The gradient (the slope of graph) of a distance-time graph represents speed.