IB Math SL Year 2 Name Date Lesson 10-4: Displacement, Velocity, Acceleration Revisited
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1 Name Date Lesson 10-4: Displacement, Velocity, Acceleration Revisited Learning Goals: How do you apply integrals to real-world scenarios? Recall: Linear Motion When an object is moving, a ball in the air for example, we can use functions and calculus to analyze its displacement, velocity, and acceleration. Displacement- position (distance from original location) Velocity - speed in a given direction over time; change in positioning over time Acceleration - change in the rate of speed (or the change in velocity). *note, calculator should be in radians for application questions, unless otherwise specified! 1. The velocity, v, in meters per second of a particle moving in a straight line is given by:, where t is time in seconds. a) Find the acceleration of the particle at t = 1 b) Find the displacement of the particle traveled between 2 seconds and 8 seconds.
2 2. A particle moves in a straight line. Its velocity after t seconds is given by a. After p seconds, the particle is 2 m from its initial position. Find the possible values of p b. Determine the acceleration of the particle after 1 second
3 Group Practice Warm-Up 1. The velocity, v(t), of a ball in feet per second line is given by:, where t is time in seconds. a) Write an integral to express the displacement of the ball over the first four seconds. b) Hence, find the displacement of the ball over the first four seconds. 2. For the given velocity v = find the displacement between t = 0.2 and t = 0.9.
4 Practice Complete for HW 3. The acceleration a ms -2, of a particle at time t seconds is given by: Given that the particle is at rest (which means velocity is ) when t = 1. Determine the function for velocity. Hence, find the velocity of the particle when t = For the given velocity v = find the displacement traveled between t = and t =.
5 5. The following diagram shows the graph of the displacement, velocity, and acceleration of a moving particle as functions of time, x. a. Complete the following table by noting which graph I, II, or III corresponds to each function: Function Displacement Acceleration Graph b. Write down the value of t when the velocity is the greatest. 6. A rocket moving in a straight line has a velocity of v km/s and displacement s km at time t seconds. The velocity v is given by v(t) = 6e 2t + t. When t = 0, s = 10. Find an expression for the displacement, s, of the rocket in terms of t.
6 7. A particle moves in a straight line. Its velocity, v ms -1 at time t seconds is given by: a. Find the velocity of the particle when t = 1 b. Find the value of t for which the particle is at rest. c. Show that the acceleration of the particle is given by:
7 8. The velocity, v, in meters per second of a particle moving in a straight line is given by:, where t is time in seconds. a) Find the acceleration of the particle at t = 1 b) Find the displacement of the particle traveled between 2 seconds and 8 seconds. (calculator only for final answer, show all calculus)!
8 9. A particle moves in a straight line with velocity, for t, where v is in centimetres per second and t is in seconds. a. Find the acceleration of the particle after 2.7 seconds. b. Find the displacement of the particle after the first 1.3 seconds. 10. If f (x) = cos x, and f = 2, find f (x). 2
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