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Velocity Functions

Velocity Functions. “Today were going to play a game of solving velocity functions.”. The Problem. A squirrel starts at building A at time t = 0 and travels along a straight wire connected to building B. For 0 ≤ t ≤ 18, the squirrel’s velocity is modeled by the piecewise-linear function

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Velocity Functions

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  1. Velocity Functions “Today were going to play a game of solving velocity functions.”

  2. The Problem A squirrel starts at building A at time t = 0 and travels along a straight wire connected to building B. For 0 ≤ t ≤ 18, the squirrel’s velocity is modeled by the piecewise-linear function defined by the graph above. (a) At what times in the interval 0 < t < 18, if any, does the squirrel change direction? Give a reason for your answer. (b) At what time in the interval 0 ≤ t ≤ 18 is the squirrel farthest from building A ? How far from building A is the squirrel at this time? (c) Find the total distance the squirrel travels during the time interval 0 ≤ t ≤ 18. (d) Write expressions for the squirrel’s acceleration a(t ), velocity v(t ), and distance x(t ) from building A that are valid for the time interval 7 < t < 10.

  3. How to solve the problem: 1] Graphically 2] Numerically 3] Algebraically 4] Verbally

  4. Part A(a) At what times in the interval 0 < t < 18, if any, does thesquirrel change direction? Give a reason for your answer.The squirrel changes direction when its velocity changes sign at any time.This occurs at t = 9 and t = 15.

  5. Part B • (b) At what time in the interval 0 ≤ t ≤ 18 is the squirrel farthest from building A ? How far from building A is the squirrel at this time? • I used Area of Trapezoid= • Base 1 + Base 2 multiply by height divide by 2

  6. Part C • (c) Find the total distance the squirrel travels during the time interval 0 ≤ t ≤ 18. • The total distance traveled is140+25+50=215

  7. Part D(d) Write expressions for the squirrel’s acceleration a(t ), velocity v(t ), and distance x(t ) from building A thatare valid for the time interval 7 < t < 10.I used the slope formula= y2-y1 over x2-x1

  8. The EndMiami Heat NBA Champions

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