Question:
If a particle has velocity v(t) = 8 m/sec. What is its position x(t) for the following to cases
        (a)     x(t = 10 sec) = 100 m?
        (b)     x(t = 10 sec) = 5 m
?

 

Answer:
We will present two methods to solve this problem


Method 1:

   We know from a previous question, if  x(t) = c1 + c2 t, then v(t) = c2.  So we know  that x(t) is a straight line with a slope given by v(t) = c2= 8 m/sec.  We need to find  c1.

                           

        (a)     x(t=10) = 100 = c1 + 8 (10)
  
                           c1 = 100 - 80 = 20 m
                Thus x(t) = 20 + 8 t.

 

        (b)     x(t=10) = 5 = c3 + 8 (10)
  
                         c3 = 5 - 80 = -75 m.
                 Thus x(t) = -75 + 8 t.


Method 2 ( General) :                    Math Refresher