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Introduction to Definite Integrals
8. Definite Integrals / Introduction to Definite Integrals / Problem 4
Problem 4

A cyclist's velocity (in mi/hr\(\text{mi/hr}\)) is described by the following piecewise function for a 22-hour ride. Find the function that gives the displacement of the cyclist over the interval [0,t][0, t], where 0≤t≤20 \(\leq\) t \(\leq\) 2.
v(t)={18if 0≤t≤124if 1<t≤1.520if 1.5<t≤2v(t)=\(\begin{cases}\)18 & \(\text{if }\)0\(\leq\) t\(\leq\)1\\ 24 & \(\text{if }\)1<t\(\leq\)1.5\\ 20 & \(\text{if }\)1.5<t\(\leq\)2\(\end{cases}\)
What is the displacement function s(t)s(t)?