In a velocity - time graph how (i) uniform retardation , (ii) gradually increasing retardation and (iii) gradually decreasing retardation can be represented ?

Explanation

In a velocity-time graph a negative slope represents the rate of decrease in velocity with time.
(i) In case of uniform retardation the slope is constant and the graph is a straight line with a negative slope as shown by line 1 in Fig 1.42.
(ii) In case of gradually increasing retardation the magnitude of slope increases gradually. Thus the graph is a curved line ,as shown by line 2 in Fig 1.42.
(iii) In case of gradually decreasing retardation the magnitude of slope will decrease gradually. The graph is a curved line (line 3) in Fig 1.42. In each case OA represents the initial velocity.