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Understanding Differentiation and Integration of Particle Motion

This guide explores the principles of differentiation and integration in relation to particle motion along a line. It covers the concepts of position, velocity, and acceleration, alongside the application of the product and quotient rules. The section includes practical problems, such as finding the particle's position at a given time, its initial velocity, and acceleration. Additionally, it addresses concepts like instantaneous versus average velocity and discusses Pythagorean and double angle identities, making it a comprehensive resource for students of calculus.

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Understanding Differentiation and Integration of Particle Motion

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  1. Section 4.2 – Differentiating Exponential Functions Section 4.3 – Product Rule/Quotient Rule THE MEMORIZATION LIST BEGINS

  2. Find

  3. DIFFERENTIATE POSITION s(t) VELOCITY v(t) ACCELERATION a(t) INTEGRATE

  4. No Calculator A particle moves along a line so that at time t, 0 < t < 5, its position is given by a) Find the position of the particle at t = 2 b) What is the initial velocity? (Hint: velocity at t = 0) c) What is the acceleration of the particle at t = 2

  5. CALCULATOR REQUIRED Suppose a particle is moving along a coordinate line and its position at time t is given by For what value of t in the interval [1, 4] is the instantaneous velocity equal to the average velocity? a) 2.00 b) 2.11 c) 2.22 d) 2.33 e) 2.44

  6. then

  7. NO CALCULATOR An equation of the normal to the graph of

  8. NO CALCULATOR

  9. NO CALCULATOR

  10. NO CALCULATOR

  11. NO CALCULATOR Consider the function A) 5 B) 4 C) 3 D) 2 E) 1

  12. ADD TO THE MEMORIZATION LIST

  13. NO CALCULATOR

  14. The Basics Pythagorean Identities Double Angle Identities

  15. NO CALCULATOR At x = 0, which of the following is true of • f is increasing • f is decreasing • f is discontinuous • f is concave up • f is concave down X X X

  16. NO CALCULATOR If the average rate of change of a function f over the interval from x = 2 to x = 2 + h is given by A) -1 B) 0 C) 1 D) 2 E) 3

  17. NO CALCULATOR The graph of has an inflection point whenever

  18. NO CALCULATOR then an equation of the line tangent to the graph of F at the point where

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