# Velocity Time Graph

- Calculation of distance using velocity time graph
- Velocity time graph of object in uniform acceleration
- Calculation of displacement and distance

The slope of a Velocity–time graph of an object moving in rectilinear motion with uniform velocity is straight line and parallel to x-axis when velocity is taken along y-axis and time is taken along x-axis.

### Calculation of distance using velocity-time graph:

Let two points A and B on the slope of graph.

Draw two lines parallel to y-axis AC from point A, and BD from point B.

Let point D at the x-axis (time axis) is t2 and point C is t1.

Let AB meet at ‘v’ at y-axis, i.e. object is moving with a velocity, v.

Thus, distance or displacement by the object is equal to the area of the rectangle (shaded) ABCD.

Thus, Area of `ABCD = BD xx DC`

`=> s = v (t_2 – t_1)`

Since given object is moving with constant velocity along a straight line, thus displacement will be equal to distance covered.

Therefore, Distance or Displacement = velocity X time interval.

## Velocity Time Graph of an object moving with uniform acceleration

When velocity – time graph is plotted for an object moving with uniform acceleration, the slope of the graph is a straight line.

The pattern of slope of the graph shows that object is moving with uniform acceleration.

### Calculation of Displacement and Distance covered by the moving object using velocity time graph:

Let take two points, A and B at the slope of the graph.

Draw a line from B to BD and another from point A to AE parallel to y-axis.

Let AD meets at `t_2` and `AE` at `t_1` on the time axis.

Thus, Distance covered by the object in the given time interval `(t_2 – t_1)` is given by the area of ABCDE.

Therefore, Distance (s) = Area of `Delta ABCD +` Area of `ACDE`

`=>S=1/2 xx BC xx AC + (AExxED)`

Displacement of the object during the given time interval `(t_2-t_1)` = Area of ACDE

Thus, Displcement `= AE xx ED`

### Velocity time graph of an object moving with uniform decreasing velocity:

The slope of the velocity time graph of an object moving with uniform decreasing velocity with uniform acceleration is a downwards straight line. The straight downward slope shows the decreasing velocity with uniform acceleration, i.e. retardation.

#### Velocity time graph of an object moving with non-uniform velocity:

Zig–zag line of slope of graph shows that the object is moving with non-uniform velocity.