Question

A person is walking along a straight line. Her velocity function(in meters per second) is given by v(t)=3t-6, 0<=t<=3. Find (a) the displacement, and (b) the distance travelled by this person over the 3 seconds

Note: the answers to the two questions are different. Figuring out what they mean is part of the problem.@calculus

Answer 1

\[v(t)=3t-6\quad,\quad 0\leq t\leq 3\](a)\[x(t=3)=\int\limits_0^3(3t-6)dt=-4.5\](b)\[s(t=3)=\int\limits_0^3|3t-6|dt=\int\limits_0^2(6-3t)dt+\int\limits_2^3(3t-6)dt=\]\[=6+1.5=7.5\]