1) A particle has position p (in meters) at time t(in seconds): p = t"-4t+1 a) between t=0 and t=5, find the displacement (change in position) and the velocity b) Find the velocity at time t. c) What is the velocity at the 5 second mark? d) What is the acceleration at the 5 second mark? 2) A thrown ball has height h = 24t 4.9[2 [h in meters, tin seconds] a) when is the ball on the ground? b) when is the ball not moving? c) when is the ball moving upwards? 3) Computer chips are sometimes made from a square of silicon. a) write the formula for the area A as a function of the side length 5. b) as the side length goes from 15mm to 17mm, what is the change in area? What is the average rate of _ change of area relative to side? c) what is the infinitesimal rate of change of the area for side length 15mm? 4) For a circle, find the rate of change of the area relative to radius a) as the radius goes from 3 to 3.5 b) when the radius is exactly 3 5) A spherical cell is growing. [for a sphere, V= .7! r3 ] Find the rate of change for the cell volume with respect to radius a) when the radius changes from 6 to 8 pm . b) when the radius changes from 6 to 6.1 pm c) when the radius is exactly 6pm (1) give the infinitesimal rate equation and change equation 6) The mass of the part of a metal rod that lies between its left end and a point x meters to the right is 3x2 kg. Find the linear density (the rate of mass per length) for the rod 3) between x=1 and x=3 b) at the 1m mark 7) If a tank has a capacity C gallons of water, which drains completely from the bottom of the tank in D minutes, then Torricelli's Law gives the volume V of water remaining in the tank after t minutes as t 2 V=C (13) Suppose a tank has capacity C=5000 gallons and can drain completely in D=40 minutes. a) what is the volume at t=5? b) what is the volume at t=10? in ~ c) what is the change in volume from t=5 to t=10? d) what is the rate of change of the volume relative to time from t==5 to Flt)? e) what is the rate of change of the volume relative to time at 1:25 ? 1