By: Hawa Soumare.  Question   Part A: Finding zeros  Part B: Integration  Part C: Interpreting graphs  Part D: Finding derivative and comparison.

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Presentation transcript:

By: Hawa Soumare

 Question

  Part A: Finding zeros  Part B: Integration  Part C: Interpreting graphs  Part D: Finding derivative and comparison Plan

  First, set |V(t)| = 2. Which you then change to |V(t)| - 2 = 0. You plug this into the calculator, graph it, and find the zeros between the interval 2 ≤ t ≤ 4 Part A: Find all values of t in the interval 2 ≤ t ≤ 4 for which the speed of the particle is 2.

  We can find s(5) by plugging in 5 for t  Remember it is given that s(0) = 10 Part B: Write an expression involving an integral that gives the position s ( t ). Use this expression to find the position of the particle at time t = 5.

  The particle will change direction when v(t) changes signs. You graph v(t) between 0 ≤ t ≤ 5 and see where it passes the x-axis. This occurs at t = and t = v ( t ) changes sign from negative to positive at time t = v ( t ) changes sign from positive to negative at time t =  Therefore, the particle changes direction at time t = and time t = (or 3.317). Part C: Find all times t in the interval 0 ≤ t ≤ 5 at which the particle changes direction. Justify your answer.

  Speed is increasing when the signs of v(t) and a(t) are the same and decreasing when the signs are different  Using the calculator you will find: Part D: Is the speed of the particle increasing or decreasing at time t = 4 ? Give a reason for your answer.

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