Imagine dropping a steel ball bearing into a tall cylinder full of mineral oil. Viscous drag has a significant effect on the ball bearing's downward velocity, v(t). One family of dynamic models for this takes the form()dvdt=gkvp,where g is the acceleration of gravity and k is a constant. The size of k is related to the viscosity of the medium: when k=0, equation () is the familiar friction-free approximation for a falling mass. The exponent p is an interesting topic for dicussion: for this problem we consider p=1.In this problem, we use SI units, so t is in seconds, v is in metres per second, etc. Use the international standard valueg=9.807 and assume mineral oil has viscosity parameter k=20.(a) Find v(t). (Assume v(0)=0.)v(t)=

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(b) Let y(t) denote the distance the ball bearing has dropped at time t. (This terminology entails y(0)=0, and y(t)>0 for t>0.) Find y(t).y(t)=

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(c) Using computer assistance as appropriate, find the time required for the ball bearing to drop 1 metre from its release point.y(t)=1 when t=