1. Prove that f'(x) is the first derivative of f(x).5x23f'(x) = x² - 1*x²-1f(x) = x*x²2. Find the law of motion of an object acted upon by a constant force F:a. If at time t = 0, the body is at rest at the origin (x = 0).b. If x(t = 0) = 0, v(t = 0) = vo⋅c. If x(t = 0) = xo, v(t = 0) = v0.3. The potential energy is given by the formula u = x² (k > 0). Construct a graph andshow that the motion is oscillatory.

Answered: 1. Prove that f'(x) is the first…

Glencoe Physics: Principles and Problems, Student Edition

1st Edition

ISBN:9780078807213

Author:Paul W. Zitzewitz

Publisher:Paul W. Zitzewitz

Chapter6: Motion In Two Dimensions

Section6.3: Relative Velocity

Problem 27PP

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3. The velocity of the body is given by V(t)=sin(xt), where the velocity is given in m/s and t is in seconds. The distance covered in meters between t=1/4 and ½ seconds is close to: A. -0.225 С. 1.2251 В. 0.225 D. 1 4. Evaluate the integral of xy with respect to y and to x, for the limits from x=0 to x=1, and the limits from y=1 to y=2. A. 7/9 C. % B. % D. 5/8
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1. a. A runner starts from rest and in 2 s reaches a speed of 10 m/s. If we assume that the speed changed at a constant rate (constant net force), what was the average speed during this 2 s interval? -average speed=_______m/s b. How far did the runner go in this 2 s interval? - distance= _____m 2. Which of the following descriptions best describes the motion map of a tennis ball rolling off a table? a. The y velocity arrows stay the same length. b. The y velocity arrows get longer. c. The x velocity arrows get longer. d. The x velocity arrows stay the same length e. The y velocity arrows get shorter. f. The x velocity arrows get shorter
6. Consider the velocity-time graph shown below. Which section has the smallest v (m/s) D LA + + + 1 2 3 4 5 6 7 8 9 B 4 3 2 1 -1 -2 -3 -4 t(s) magnitude of velocity? know Explain how you this using only words (no calculations)
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2. The motion of a body falling in a resisting medium may be described by dv mt=mg - bv when the retarding force is proportional to the velocity, v. a. Find the velocity. b. Evaluate the constant of integration by demanding that v(0) = 0. Explain the signs of the terms mg and bv. C.
The simplest SI unit of Q, if Q= Forcex Areax Time /Mass x velocity is a. m^4 O b. m O c. m^3 O d. m^2
1. Draw a vector to represent each of the following physical quantities. Choose an appropriate coordinate system. a. A displacement of 40 km in the negative y-direction. b. A velocity of 30 m/s at 5° below the negative x-axis. C. An acceleration of 5 m/s² due east. d. A force of 30 N at 15° south of west.
A car is driving along a circular track of diameter d = 0.75 km at a constant speed of v = 22 m/s.a. Write an expression for the magnitude of acceleration a of the car in terms of the given parameter. b. What is the magnitude, in meters per second squared, of the acceleration a of the car. c. Write an expression for the minimum coefficient of the friction μ between the car's tires and the road that is required in order to keep the car going in a circle in terms of the given parameters.
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