Question 3 A speed-boat accelerates from rest (with increasing velocity), reaching a speed of 40 m/sec as it moves in a straight line over a period of 20 seconds. Velocities were measured every 2 seconds, and recorded in the following table: time (sec) 024 6 8 10 12 14 16 18 20 vel (m/sec) 038 13 19 25 29 33 36 38 40 Use lower and upper Riemann sums to find lower and upper bounds for the distance travelled by the boat.

If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per second. What is the terminal velocity, and how long does it take the filter to reach 99 of terminal velocity? Use a table increment of 0.1 and given your answer to the nearest tenth of a second.

A mass weighing 64 pounds stretches a spring 0.32 foot.The mass is initially released from a point 8 inches above theequilibrium position with a downward velocity of 5 ft/s.(a) Find the equation of motion.(b) What are the amplitude and period of motion?(c) How many complete cycles will the mass have completedat the end of 3 seconds?(d) At what time does the mass pass through the equilibriumposition heading downward for the second time?(e) At what times does the mass attain its extremedisplacements on either side of the equilibrium position?(f) What is the position of the mass at t 5 3 s?(g) What is the instantaneous velocity at t 5 3 s?(h) What is the acceleration at t 5 3 s?(i) What is the instantaneous velocity at the times when themass passes through the equilibrium position?(j) At what times is the mass 5 inches below the equilibriumposition?(k) At what times is the mass 5 inches below the equilibriumposition heading in the upward direction?