# Distance Time Graph

- Calculation of velocity using distance time graph
- Distance time graph of a body in accelerated motion

When an object is moving with uniform velocity, the slope of graph is always a straight line. In other words slope of straight line of a distance-time graph shows that object is moving with uniform velocity.

In the above graph, straight slope line shows that object is moving with uniform velocity. Slope OB shows the velocity of the object.

## Calculation of Velocity using distance-time graph:

To calculate the velocity, let take two points A and B on the slope OB.

Draw one line parallel to y-axis and another parallel to x-axis from B.

Again draw a line parallel to y-axis and another parallel to x-axis from point A.

Let, line parallel to x-axis from point B cut at a point, S2 at y-axis.

Line parallel to x-axis from point A cut at point, S1 at y-axis.

Let, line parallel to y-axis from point B cut at t2 at x-axis.

Line parallel to y-axis from point A cut at t1 at x-axis.

Now, BC= Distance = S2 – S1 and AC = time = t2 – t1

We know that slope of the graph is given by the ratio of change in y-axis and change in X-axis.

Or, Slope = (text{Change in y-axis})/(text{Change in x-axis})`

Thus, slope, `AB=(BC)/(AC)`

Or, `v=(s_2-s_1)/(t_2-t_1)`

Where, `v`= velocity, `(s_2-s_1)` = interval of distance and `(t_2-t_1)` = time interval

Thus, `text{velocity}=text{Distance}/text{Time}`

## Distance – Time Graph of a body moving with Accelerated motion:

When graph of distance Vs time is plotted for an object moving with accelerated motion, i.e. with increasing non-uniform speed, the slope of graph will not be a straight line. The rising trend of slope shows the increasing trend of velocity.