Which graph in Fig. best shows the velocity-time graph for an object launched vertically into the air when air resistance is given by D = bv? The dashed line shows the velocity graph if there were no air resistance.

The correct option is: (B).
Assume that the mass of object launched is m , the acceleration due to gravity is g and the acceleration of the object at any instant is a.
Using Newton’s second law of motion,


Divide numerator and denominator of the term on the left hand side by m,


It is important to note that we assume initial conditions such that the constant of integration C is zero.


Only curve (B) given below accounts for the fact stated above.

Therefore (B) is velocity time graph for the object going upward under the air resistance, and is the correct option in this case.