The velocity v(t)v(t)v(t) of a microscopic probe moving through a fluid is modeled by the function
v(t)=10t2−34t,t>0 v(t) = \frac{10t^2 - 3}{4\sqrt{t}}, \quad t > 0 v(t)=4t10t2−3,t>0where vvv is measured in μm s−1\mu\text{m s}^{-1}μm s−1 and ttt is the time in seconds. At time t=1t = 1t=1, the displacement of the probe from a fixed origin is 4μm4 \mu\text{m}4μm. Find the displacement of the probe when t=9t = 9t=9.
