Calculus II, MA 112
WorkSheet 1
December 1, 1998
1) Find the general solution (this means a constant will be in your answer) to the di¤erential
dy
equation
= 3 cos(4x) ¡ x
dx
2) Find the solution to the initial value problem (IVP – this means a di¤erential equation
dy
with some condition about the function)
= 3x2 ¡ 5x + e2x ; y(0) = 5
dx
1
3) A particle moves along the x–axis with velocity function v(t) = p : At time t = 1;
t
the position of the particle is at x = 4: Find the acceleration a(t) and the position of the
function x(t): How far does the particle travel in the time interval t = 1 to t = 3? What is
the particle’s average velocity in the time interval t = 1 to t = 3?
4) Assume that a ball which weighs 1/3 lb is thrown upward from the top of a 50 foot
building with a speed of 65 ft/sec. How high does the ball go and when does it hit the
ground? Start the solution to this problem with Newton’s second law (F = ma):
5) Same ball and building as in (4) but now the ball is initially thrown downward with a
speed of 70 ft/sec. What is the speed with which the ball hits the ground? Again start with
Newton’s second law.