The acceleration of an object (in m/s^2) is given by the function a(t) = 9 sin(t). The initial velocity of the object is v(0) =
-11 m/s. a) Find an equation v(t) for the object velocity v(t) =___________b) Find the object's displacement (in meters) from time 0 to time 3 meters c) Find the total distance traveled by the object from time 0 to time 3 meters
a) Acceleration is the derivative of velocity. By the fundamental theorem of calculus,
so that
b) We get the displacement by integrating the velocity function like above. Assume the object starts at the origin, so that its initial position is . Then its displacement over the time interval [0, 3] is
c) The total distance traveled is the integral of the absolute value of the velocity function:
for and for , so we split the integral into two as