CALCULUS QUESTIONS 9. A boat of mass m = 540 kgs moves horizontally on the water surface at a constant speed of 7 m/s. At time t=0 the motor is turned off and the boat is subject to a horizontal frictional resistance force, f(t)=-bv(t), where b is a constant with units kg/s and v(t) is the instantaneous velocity of the boat. Assume that the boat begins its motion with an initial speed of vo= v(0) = 7 m/s at the position x = 0 at time t = 0. (a)()Use Newton's 2nd Law to find the first order equation for v(t) which satisfies the initial condition v(0) = 7 m/s. Write the solution for v(t) which fits the initial condition. (You can check it by differentiation.) from the Sun. The (b)( ) Using the value of m = 540kgs, find the value of b, given the information that at time t = 6 seconds, v(6) = 0.95 m/s. c(. Write v(t) = dx/dt = your solution in (a). Use this 1st order equation to find x(t) by indefinite integration remembering to add a constant C. Evaluate C using the initial condition x(0) = 0. (d) Is there an upper limit to x(t) even though v(t)is never 0? Make rough sketches of v(t) and x(t) vs time t. What is the maximum distance covered in an infinite time? (Use the numbers given in the problem.)

CALCULUS QUESTIONS 9. A boat of mass m = 540 kgs moves horizontally on the water surface at a constant speed of 7 m/s. At time t=0 the motor is turned off and the boat is subject to a horizontal frictional resistance force, f(t)=-bv(t), where b is a constant with units kg/s and v(t) is the instantaneous velocity of the boat. Assume that the boat begins its motion with an initial speed of vo= v(0) = 7 m/s at the position x = 0 at time t = 0. (a)()Use Newton's 2nd Law to find the first order equation for v(t) which satisfies the initial condition v(0) = 7 m/s. Write the solution for v(t) which fits the initial condition. (You can check it by differentiation.) from the Sun. The (b)( ) Using the value of m = 540kgs, find the value of b, given the information that at time t = 6 seconds, v(6) = 0.95 m/s. c(. Write v(t) = dx/dt = your solution in (a). Use this 1st order equation to find x(t) by indefinite integration remembering to add a constant C. Evaluate C using the initial condition x(0) = 0. (d) Is there an upper limit to x(t) even though v(t)is never 0? Make rough sketches of v(t) and x(t) vs time t. What is the maximum distance covered in an infinite time? (Use the numbers given in the problem.)