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An object is releaseed 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(1-e^bt) / b

b) v = (g+a)t / b

c) v = (ge^bt) / b

c) v = gt - bt^2

d) v = v_0 + gt, v_0 does not = 0

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The velocity of a particle moving along the x-axis is given by:

v = at - bt^3 for t > 0

a = 31m/s^2, b = 2.5 m/s^4, and t is in seconds.

What is the acceleration a, of the particle when it achieves its maxiumum displacement in the positive x direction? Answer in units of m/s^2.

a) v = g(1-e^bt) / b

b) v = (g+a)t / b

c) v = (ge^bt) / b

c) v = gt - bt^2

d) v = v_0 + gt, v_0 does not = 0

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The velocity of a particle moving along the x-axis is given by:

v = at - bt^3 for t > 0

a = 31m/s^2, b = 2.5 m/s^4, and t is in seconds.

What is the acceleration a, of the particle when it achieves its maxiumum displacement in the positive x direction? Answer in units of m/s^2.

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