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Motion Graphs

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Graphs are mathematical models. They are a very useful way of describing relationships. Graphs are especially useful when describing the motion of the objects, that is, any moving object changes is position with respect to time. The easiest way to describe the motion of a moving body is by using a graph.

The most commonly used graphs for describing linear motion of a body are
  1. Distance-time graph
  2. Displacement-time graph
  3. Speed-time graph
  4. Velocity-time graph
  5. Acceleration-time graph

Distance Time Graph

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The geometrical relationship between the distance travelled by an object and the time taken by the object is called the distance-time graph.
The distance-time graph of an object can be drown by taking the time taken along the X-axis and the distance travelled along the Y- axis. The ratio of the distance travelled and the time taken will give the speed of the object. Therefore , the slope of the distance-time graph gives the speed of the given object. That is, by using this graph one can find the speed of an object.

The distance-time graph under different conditions are given below

a) When object is at rest:

At rest the position of the object will be constant, that is the object will not change its position with respect to time. It remains at the same distance at all time. The distance-time graph for an object at rest is a straight line parallel to the time axis. And the slope of the graph will be zero.

Distance Time Graph at Rest

b) When object moving with a uniform speed:

When the object covers equal distance in equal interval of time, then said to have a uniform speed. The distance-time graph for object moving with uniform speed is a straight line having all the points falls on it. Which will make an angle with the X-axis. The slope of the graph will give the speed of an object and the slope must be same everywhere in the straight line.

Distance Time Graph at Uniform

c) When object moving with non-uniform speed:

When a body moves with non-uniform speed it covers unequal distance in equal intervals of time. The distance-time graph for a body which is moving with non-uniform speed is not a straight line. It is a curve. The speed of the object will change with respect to time.

Distance Time Graph at Nonuniform

Displacement Time Graph

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Displacement-time graph for an object depends upon the nature of motion of the body. Displacement is a vector quantity. It got both direction and magnitude. The slope of a displacement-time graph gives the velocity of the object. The slope of the displacement-time graph is zero when the object is at rest. The displacement-time graph at different conditions say, when the object is at rest, moving with uniform speed and non-uniform speed are given below.

Displacement Time Rest

Displacement Time Uniform

Displacement Time Nonuniform

Velocity Time Graph

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The geometrical relationship between the velocity of an object and the time taken by the object is called the velocity-time graph.
The velocity-time graph of an object can be drown by taking the time taken along the X-axis and the velocity along the Y-axis. The ratio of the velocity and the time taken will give the acceleration of the object. Therefore, the slope of the velocity-time graph gives the acceleration of the given object. That is, by using this graph one can find the acceleration of an object. The velocity-time graph under different conditions are shown below.

Velocity Time Rest

Velocity Time Uniform

Velocity Time Uniform

Velocity Time Initial Not Zero

Velocity time

Speed Time Graph

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The geometrical relationship between the speed of an object and the time taken by the object is called the speed-time graph. The speed-time graph of an object can be drown by taking the time taken along the X-axis and the speed along the Y-axis. The ratio of the speed and the time taken will give the acceleration of the object. Therefore, the slope of the speed-time graph gives the acceleration of the given object. That is, by using this graph one can find the acceleration of an object.

Speed Time Graph


Speed Time Uniform Acceleration


Speed Time Graph at Zero


Speed Time Non Uniform

Acceleration Time Graph

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The geometrical relationship between the acceleration of an object and the time taken by the object is called the acceleration-time graph. This can be drown by taking the time taken along the X-axis and the speed along the Y- axis.

Acceleration-time graph when the acceleration is constant

Acceleration Graph

Acceleration-time graph for non-uniform changes
Graph of Acceleration Example

Acceleration-time graph for uniform changes
Graph of Acceleration