Question

An object is released from rest at time t = 0 and falls through the air, which exerts a resistive force such that the acceleration a of the object is given by a = g – bV, where V is the object's speed and b is a constant. If limiting cases for large and small values of t are considered, which of the following is a possible expression for the speed of the object as an explicit function of time?
a. v = g(l - e-bt)/b.
b. v = (gebt)/b.
c. v = gt - bt2.
d. v = (g + a)t/b.
e. v = V0 + gt, v0.

Answer 1

Answer:

The correct option is

a. v = $g (1-e^{-bt})/b$

Explanation:

Time at which the object start fall t = 0

The acceleration a is given by a = g - bV

Where V = Speed of the object

Speed V² = u² + 2·a·h

However with the drag force the object will approach terminal velocity as t becomes progressively larger whereby v will stop increasing

Option a. is the only option that has  limiting value of v which is in the range of g as t increases ∴ option a. is the correct option.

v = $g (1-e^{-bt})/b$  as t increases $(1-e^{-bt})$ → 1 s and v→ g/b m/s