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Velocity Functions

In this game of solving velocity functions, we explore the movement of a squirrel traveling between two buildings. The problem consists of multiple parts: determining when the squirrel changes direction, finding the point farthest from building A, calculating the total distance traveled, and expressing its acceleration, velocity, and distance. We use graphical, numerical, algebraic, and verbal methods to analyze the piecewise-linear velocity function. Join us in dissecting this interesting motion scenario and uncover the dynamics of the squirrel's journey!

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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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