A molecule slows down during fibril growths Motion of a molecule toward a growing fibril.

Question A molecule is moving a short distance toward a fibril to help it grow. The molecule’s motion is so important that we make a movie and measure it carefully. We then fit an equation to the data that turns out to be the following, where all the units are in micro-meters : x=(24t-2ttt) Using calculus, we can calculate v and a. Calculate the rate at which the particle is slowing down when it lands on the fibril and stops. a. 0; b. 8; c. 16; d. 32; e. 24;

Create the step by step solution 1.Sketch (no geometry or unit change) 2.List the variables we know and want: 3.Calculus Equation(s) 4.Algebra 5.Arithmetic 6.Answer letter:

Create the step by step solution 1.Sketch (no geometry or unit change) 2.List the variables we know and want: x, v=?, t=?, a=? 3.Math equation for v: v=dx/dt=d[24t-2t 3 ]/dt=24-6t 2 4.Algebra: v=24-6t 2 =>v-24=-6t 2 => t=sqrt[(24-v)/6] 5.Arithmetic: t=sqrt[(24+0)/6] => t=2 6.Math for a: a=dv/dt=0-12t 7.Arithmetic: a=-12*2 8.Answer letter: e Comment: Problems like this get stuck in our exams because calculus is sometimes useful. v t