A blimp is initially at rest, hovering, whenat t = 0 the pilot turns on the moto

Question

A blimp is initially at rest, hovering, whenat t = 0 the pilot turns on the motor of the propeller. Themotor cannot instantly get the propeller going, but the propellerspeeds up steadily. The steadily increasing force between the airand the propeller is given by the equationF = kt, wherek is a constant. If the mass of the blimpis m, find its position as a function of time. (Assumethat during the period of time you're dealing with, the blimp isnot yet moving fast enough to cause a signi cant backward force dueto air resistance.)

Explanation / Answer

Use the equation of motion: x = v0*t + (1/2)*a*t2 But since the blimp is initially at rest, v0 = 0: x = (1/2)*a*t2 Use F = ma to solve for a: a = F / m And the problem says that F = kt, so we get: a = kt / m Putting that back into the green equation above: x = (1/2)*(kt / m) * t2 Simplifies to: x = kt3 / 2m

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