### Theory:

Let us consider a bus travelling from Chennai to Trichy. The speed of the bus is measured for every second. The speed and time are recorded, and a graph is plotted using the data. The results for six possible journeys are shown below.

Case I: Bus at rest:

 Time($$s$$) $$0$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ Speed($$m/s$$) $$0$$ $$0$$ $$0$$ $$0$$ $$0$$ $$0$$ Case II: Bus travelling at uniform speed:

 Time($$s$$) $$0$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ Speed($$m/s$$) $$10$$ $$10$$ $$10$$ $$10$$ $$10$$ $$10$$ Case III: Bus travelling at uniform acceleration:

 Time($$s$$) $$0$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ Speed($$m/s$$) $$0$$ $$10$$ $$20$$ $$30$$ $$40$$ $$50$$ Case IV: Bus travelling at uniform deceleration:

 Time($$s$$) $$0$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ Speed($$m/s$$) $$50$$ $$40$$ $$30$$ $$20$$ $$10$$ $$0$$ Case V: Bus travelling with increasing acceleration:

 Time($$s$$) $$0$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ Speed($$m/s$$) $$0$$ $$2$$ $$8$$ $$18$$ $$32$$ $$50$$ Case VI: Bus travelling with increasing deceleration:

 Time($$s$$) $$0$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ Speed($$m/s$$) $$0$$ $$18$$ $$32$$ $$42$$ $$48$$ $$50$$ 