# Motion Graphs, Distance-Time Graph for Uniform Motion, Velocity-Time Graph (For CBSE, ICSE, IAS, NET, NRA 2022)

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# Motion Graphs

- Modern mathematical notation is a highly compact way to encode ideas.
- Distance-time graph is the plot of distance travelled by a body against time. So, it will tell us about the journey made by a body and its speed.
- When it comes to depth, nothing beats an equation.
- Equations can easily contain the information equivalent of several sentences.
- Galileo՚s description of an object moving with constant speed (perhaps the first application of mathematics to motion) required one definition, four axioms, and six theorems. All of these relationships can now be written in a single equation.

## Distance-Time Graph for Uniform Motion

- Let՚s consider a distance-time graph in which the body is moving with uniform motion.
- A body is said to be in uniform motion when the body covers the equal distance in equal time intervals.
- Let՚s consider a time interval of 1 second, if a body covers 10 meters in the first 1 second then it should cover 10 meters in every second from there on, this will indicate that the body is in uniform motion.

### Moton Graph

- The distance time graph would be a straight line, because the equal distance is covered in equal units of time, as in uniform motion,
- It is because the slope of a distance-time graph determines the speed of that body, so steeper the slope greater will be the speed of the body.
- From the above graph, conclusion that body A has the highest speed and body C has the least speed.

## Distance-Time Graph for Uniformly Accelerated Motion

- The bodies had uniform motion; their velocity does not change with respect to time.
- The distance-time graph for a uniformly accelerated motion looks as shown in the graph above, consider how the distance is changing exponentially indicating that the velocity is changing at a constant rate or there is constant acceleration.
- The graph would be a straight line with its slope indicating the amount of acceleration, But in the velocity time graph as velocity changes at a constant rate with respect to time in uniformly accelerating motion

## Velocity-Time Graph

- Velocity-Time graph is the graph of velocity against time; it shows us how the velocity changes with respect to time.
- The slope of a velocity-time graph determines its acceleration.
- A flat horizontal line in a velocity-time graph states that the body is moving at a constant velocity.
- If the straight line has a slope, then that indicates the body is changing its velocity at a constant rate, or it means that the body has constant acceleration.