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.
Practise AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
