Derivatives and Graphs

Transcription

1 2 Practice nswers are available in the classroom and on the website. Scan this QR code for a direct link. I use the pp Scan on my phone erivatives and Graphs 11. particle moves in a straight line, its motion described by the equation: x(t) = 5t 2 1.2t + 2, with x in meters and t in seconds. a. Find its velocity at t = 3.0 s. b. What are the units of the coefficient 5? 12. n electron moves in a straight line given by the equation: x(t) = 2t 4 + 5t 2 + 1, with x in m and t in sec. Find its velocity at t = 1.6 s. 13. particle moves in a straight line, its motion described by the equation: x(t) = -1.3t t t, with x in meters and t in se. a. Find its acceleration at t = 1.2 s. b. What are the units of the coefficient -1.3? 14. The motion of a solid disk can be described by the equation: θ = 0.7t 2 1.2t + 8, with θ in radians and t in seconds. Find its angular speed at t = 1.2 s gram thin rod of length 60 cm rotates about an axis running perpendicular through its center. Its angular position is given by the equation: θ = 3t 2 +2t + 5, with θ in radians and t in seconds. etermine the net torque acting on it.

2 16. Use this graph of an object s position vs. time to answer the following. (a) On a position vs. time graph, what does the slope tell you about? (b) What is the position of this object at t = 2 s? (c) What is the velocity of this object at t = 2 s? (c) What is the acceleration of this object at t = 2 s? (d) Sketch the related velocity vs. time and acceleration vs. time graphs. Label key values on the axes. x = t 17. ased upon the graph shown, when should the velocity of this particle be (a) positive, (b) negative, (c) and zero? x 18. Use this graph of an object s position vs. time to answer the following. (a) On a position vs. time graph, what does the slope tell you about? (b) What is the position of this object at t = 2 s? (c) What is the velocity of this object at t = 2 s? (d) What is the acceleration of this object at t = 2 s? (e) Sketch the related velocity vs. time and acceleration vs. time graphs. Label key values on the axes. x = t t Use this graph of an object s position vs. time to answer the following. (a) escribe the object s motion during sections I, II, III, and IV. (b) This graph is unrealistic. Why? (c) raw the related velocity vs. time and acceleration vs. time graphs. an you see again why the motion is unrealistic?

3 20. box moves in a straight line given by the equation: x(t) = 2t 4 + 5t 2 + 1, with x in meters and t in seconds. Find its average velocity over the interval t = 0.4 to t = 0.7 s. 21. Look at your formula sheet if you cannot remember the formulas mentioned below. The motion of a 0.20-kilogram particle is described by the function x = 2.40t t 3, where t is in seconds and x is in meters. a. etermine the kinetic energy of the particle at t = 1.0 s. b. etermine the net force acting on the particle at t = 0.60 s. 22. system s angular position is given by θ = 5-12t + t 3, where the coefficients are radians, radians per second, and radians per second cubed, respectively. a. Find ω(t). b. etermine the object's angular position and angular velocity at t = 0.5 s. c. Find the positive time(s) when the system is at rest. d. Find the average angular velocity between times t = 1.0 and t = 1.5 s. 23. particle falls through a fluid where its velocity is given by the equation: v(t) = 14t - 3t 2, with v in m/s and t in seconds. a. What is its maximum velocity during the fall? b. Which of these functions could be the particle s position function? x(t) = 14 6t x(t) = 7t 2 t 3 x(t) = 7t 2 t spinning record can be approximated as a solid disk of mass 240 grams and diameter 30 cm. The record s angular displacement as a function of time θ(t) = 6.0t t -1.5, with θ in radians and t in seconds. a. What is the tangential acceleration of a point on the rim of the record at t = 0.80 s? b. t what time will the radial acceleration be 45 m/s 2? c. What are the units of the coefficients 6.0? 25. The force on a 0.20 kg particle as a function of time is given by the equation: F(t) = 2t + 8/t, with U in joules and x in meters. a. What is the acceleration of the particle at time t = 4.0 s? b. What is the minimum force on the particle for positive values of t?

4 Please note that the numbering restarts. Sorry but it would be too much trouble to adjust it Kinematics-Motion Graphs cart travels with a constant nonzero acceleration along a straight line. Which graph best represents the relationship between the distance the cart travels and time of travel? ase your answers to questions 2 # through on the information below. car on a straight road starts from rest and accelerates at 1.0 meter per second 2 for 10 seconds. Then the car continues to travel at constant speed for an additional 20 seconds student throws a baseball vertically upward and then catches it. If vertically upward is considered to be the positive direction, which graph best represents the relationship between velocity and time for the baseball? [Neglect friction.] etermine the speed of the car at the end of the first 10 seconds On the grid at below, use a ruler or straightedge to construct a graph of the car s speed as a function of time for the entire 30-second interval. 6. The graph below represents the displacement of an object moving in a straight line as a function of time alculate the distance the car travels in the first seconds. [Show all work, including the equation and substitution with units.] 31. What was the total distance traveled by the object during the 10-second time interval? m m m m PlusPhysics: Kinematics-Motion Graphs VEL.1,.1 Page 1

5 Kinematics-Motion Graphs Which graph best represents the relationship between the acceleration of an object falling freely near the surface of Earth and the time that it falls? Which pair of graphs represent the same motion of an object? 9. The graph below represents the velocity of an object traveling in a straight line as a function of time Which graph best represents the motion of a block accelerating uniformly down an inclined plane? 34. etermine the magnitude of the total displacement of the object at the end of the first 6 seconds. PlusPhysics: Kinematics-Motion Graphs VEL.1,.1 Page 2

6 Kinematics-Motion Graphs ase your answers to questions and on the graph below, which represents the motion of a car during a 6-second time interval 14. The graph below shows the relationship between the speed and elapsed time for an object falling freely from rest near the surface of a planet What is the acceleration of the car at t=5.0 seconds? m/s m/s m/s m/s What is the total distance traveled by the car during this 6-second interval? m m m m 39. What is the total distance the object falls during the first 3 seconds? m m m m 15. The graph below represents the relationship between speed and time for an object moving along a straight line Which graph best represents the relationship between the velocity of an object thrown straight upward from Earth s surface and the time that elapses while it is in the air? [Neglect friction.] 40. What is the total distance traveled by the object during the first 4 seconds? m m m m PlusPhysics: Kinematics-Motion Graphs VEL.1,.1 Page 3