A student integrates a velocity function v(t) and writes s(t)=∫v(t)dt+C. Which of the following best justifies how the constant C is determined?
a) Choose C=0 because adding a constant does not affect the derivative of s(t).
b) Set v(0)=0 and use that value to find C.
c) Evaluate s(t) at the time when the particle’s position is known and solve for C.
d) Differentiate s(t) twice and equate the result to v(t) to determine C.