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A tissue grows

A tissue grows. Motion of a molecule in one direction. Lashuel , Harvard. Question.

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A tissue grows

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  1. A tissue grows Motion of a molecule in one direction Lashuel, Harvard

  2. Question • We watch a molecule through a microscope as it moves around before attaching to a tissue (like a fibril) during growth. It starts at x = 2.0 micro-m (where a micro-m is 10-6m) at t = 1 s. It then moves back and forth with velocity (in micro-m/s), as shown in the graph. It moves into changed surroundings at t=3s. What is the position of the molecule (in micro-m) at t = 6.0 s? • a. −2.0; b. +2.0; c. +1.0; d. −1.0; e. 6.0; V (micro-m/s)

  3. Write the step by step solution • Sketch: 2. Check the units (leave the distances in micro-m) • List the variables we know and want: • Pick the physics equation: • Algebra • Arithmetic steps • Letter Answer v=x/t a=(v-vo)/t x=vo*t+at2/2 v2=vo2+2ax V (micro-m/s)

  4. My solution step by step 2 Parts • Sketch • Check units. • List the variables we know and want: 2 parts: x1, v1, t1, v3, t3, x3=? t6, v6, x6=? • Pick the physics equations: -1.0 -2.0 V (micro-m/s) • v=x/t sometimes: vave=(x-xo)/(t-to) • and vave=(v+vo)/2 • a=(v-vo)/t • x=vo*t+at2/2 • v2=vo2+2ax

  5. My step by step solution continued • Algebra part 1: vave=(v+vo)/2 and vave=(x-xo)/(t-to) vave=(v3+v1)/2 and vave=(x3-x1)/(t3-t1) • Arithmetic part 1: vave=2-2=0 => 0=(x3-x1)/(3-1) => x3=x1=2 • Algebra part 2: vave=(v+vo)/2 and vave=(x-xo)/(t-to) vave=(v6+v3)/2 and vave=(x6-x3)/(t6-t3) • Arithmetic part 2: vave=(0-2)/2=-1 and -1=(x6-2)/(6-3) -1*3=x6-2 => x6=-3+2=-1 • Answer: d. Comment: It really was on an exam. It’s tricky, but based on just v=x/t.

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