### Theory:

For the accelerated motion:
The distance travelled by a vehicle at a regular time interval of one second is given here.

 S. No Time ($$s$$) Distance ($$m$$) 1. $$0$$ $$0$$ 2. $$1$$ $$1$$ 3. $$2$$ $$4$$ 4. $$3$$ $$9$$ 5. $$4$$ $$16$$ 6. $$5$$ $$25$$ 7. $$6$$ $$36$$ Object moving with non-uniform speed

This graph shows the non-linear variation of the distance travelled by a vehicle with time. The shape of a graph plotted for an object travelling at a non-uniform speed is different from that of the object with uniform speed.

Example 1:
Time of arrival and departure of train at three stations $$A$$, $$B$$ and $$C$$, and the distance between station $$B$$ and $$C$$ from station $$A$$ are given in below table.

 Station Distance from A (km) Time of arrival (hours) Time of departure (hours) A 0 08:00 08:15 B 120 11:15 11:30 C 180 13:00 13:15

Plot and interpret the distance-time graph for the train, assuming that its motion between any two stations is uniform.

Solution: We should take two axis on the graph paper. The $$X$$-axis represents time, while the $$Y$$-axis represents distance.

At 8:15 distance $$=$$ $$0\ km$$
At 11:15 distance $$=$$ $$120\ km$$
At 13:15 distance $$=$$ $$180\ km$$

Example 2:
Feroz and his sister Sania goes to school on their bicycles. Both of them starts at the same time from their home but take different times to reach school although they follow the same route.

The table below shows the distance travelled by them at different times.

 Time Distance travelled by Feroz ($$km$$) Distance travelled by Sania ($$km$$) 8:00 am 0 0 8:05 am 1 0.8 8:10 am 1.9 1.6 8:15 am 2.8 2.3 8:20 am 3.6 3 8:25 am - 3.6

Plot the distance-time graph for their motions on the same scale and interpret.

Solution: Distance-time graph for their motions on the same scale plotted in the above graph.

The slope of the graph gives the speed. From the graph, it is evident that the speed of Feroz is better than Sania. Therefore, Feroz reaches before Sania and waits for her.