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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.

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.

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
6 years ago
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,

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

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It is important to note that we assume initial conditions such that the constant of integration C is zero.
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Only curve (B) given below accounts for the fact stated above.
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Therefore (B) is velocity time graph for the object going upward under the air resistance, and is the correct option in this case.

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