### Theory:

Speed – time graphs:

Let us consider you're going for a vacation with your family in a car from Chennai to Ooty.

The speed of the car is measured for every second. The speed and time are recorded and a graph is plotted using the data.

The results for four possible journeys are shown.

Case I) If the car at rest then speed will be zero for all the time.

Case II) Car travelling with uniform acceleration.

 Speed (m/s) $$0$$ $$5$$ $$10$$ $$15$$ $$20$$ $$25$$ Time(s) $$0$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$

Case III) Car travelling with increasing acceleration.

The below data shows the car travelling with increasing acceleration that is a non uniform acceleration.

 Time(s) $$0$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ Speed (m/s) $$0$$ $$2$$ $$8$$ $$18$$ $$32$$ $$50$$

From the above graph we can know that for each second the car moving $$5$$ meters.

Case IV) Car travelling with decreasing acceleration.

The below data shows the travelling with decreasing acceleration in a non uniform acceleration.

 Time(s) $$0$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ Speed (m/s) $$0$$ $$19$$ $$31$$ $$41$$ $$48$$ $$50$$