Newton's Second Law of Motion
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Suppose that a body moves in a straight line through a resisting medium with resistance proportional to the square of it's speed v with initial speed v_0 and initial position x_0. Show that it's speed and position are given by v(t)=v_0/(1+v_0kt), x(t)=x_0+((ln(1+v_0kt))/k). Conclude that the body travels only an infinite distance, i.e. x(t) tends to infinity as t tends to infinity.
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Solution Summary
Newton's Second Law of Motion is clearly evaluated in this case.
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Suppose, x(t) is the position of the body, v(t)=x'(t) is then its velocity, and x''(t) is its acceleration. According to Newton's Second Law of Motion, the acceleration of the body is given by the equation
F=ma
where F is the force acting on the body. We have the force of resistance of the medium, which is proportional to the ...
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