MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions
Problem
During a science exhibition, a robot moves along a straight line. Its displacement from the starting point after t seconds is modeled by the polynomial s(t)=2t3−9t2+12t+4 (in metres). The robot repeats a basic movement cycle whose displacement, measured from the start of each cycle, is represented by c(t)=t2−3t+2 (in metres).
(a) Write an expression that relates s(t) to c(t), the number of complete cycles covered in t seconds, and the leftover displacement.
(b) Determine the quotient and the remainder when s(t) is divided by c(t).
(c) Using your result from part (b), find how many complete cycles the robot finishes and how many metres of the next cycle remain unfinished after t=5 seconds.