Theory:

For 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 ($$t$$). 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:
The time of arrivals and departures of a train at three stations $$A$$, $$B$$ and $$C$$ and the distance of stations $$B$$ and $$C$$ from station $$A$$ are given in the 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 axes 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 go to school on their bicycles. Both of them start at the same time from their home but take different times to reach the 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

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