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(\(m/s\))\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)
 
graph 6.svg
  
Case II: Bus travelling at uniform speed:
 
Time(\(s\))\(0\)\(1\)\(2\)\(3\)\(4\)\(5\)
Speed(\(m/s\))\(10\)\(10\)\(10\)\(10\)\(10\)\(10\)
 
graph 5.svg
  
Case III: Bus travelling at uniform acceleration:
 
Time(\(s\))\(0\)\(1\)\(2\)\(3\)\(4\)\(5\)
Speed(\(m/s\))\(0\)\(10\)\(20\)\(30\)\(40\)\(50\)
 
graph 4.svg
  
Case IV: Bus travelling at uniform deceleration:
 
Time(\(s\))\(0\)\(1\)\(2\)\(3\)\(4\)\(5\)
Speed(\(m/s\))\(50\)\(40\)\(30\)\(20\)\(10\)\(0\)
 
graph 3.svg
 
Case V: Bus travelling with increasing acceleration:
 
Time(\(s\))\(0\)\(1\)\(2\)\(3\)\(4\)\(5\)
Speed(\(m/s\))\(0\)\(2\)\(8\)\(18\)\(32\)\(50\)
 
graph 2.svg
  
Case VI: Bus travelling with increasing deceleration:
 
Time(\(s\))\(0\)\(1\)\(2\)\(3\)\(4\)\(5\)
Speed(\(m/s\))\(0\)\(18\)\(32\)\(42\)\(48\)\(50\)
 
graph 1.svg