The motion of a cart attached to a horizontal spring is described as x= (0.17 m)sin[(pi* s-1 )t]. Write an expression for the cart's velocity as a function of time.
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The motion of a cart attached to a horizontal spring is described as x= (0.17 m)sin[(pi* s-1 )t]. Write an expression for the cart's velocity as a function of time.
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- Calculate the result for each of the following cases using the correct number of significant figures. a. 3.07670 10.988 b. 1.0093 105 9.98 104 c. 5.44231064.008103Figure 1.19 shows two vectors lying in the xy-plane. Determine the signs of the x- and y-components of A, B, and A+B.A pirate has buried his treasure on an island with five trees located at the points (30.0 m, 20.0 m), (60.0 m, 80.0 m), (10.0 m, 10.0 m), (40.0 m, 30.0 m), and (70.0 m, 60.0 m), all measured relative to some origin, as shown in Figure P1.69. His ships log instructs you to start at tree A and move toward tree B, but to cover only one-half the distance between A and B. Then move toward tree C, covering one-third the distance between your current location and C. Next move toward tree D, covering one-fourth the distance between where you are and D. Finally move toward tree E, covering one-fifth the distance between you and E, stop, and dig. (a) Assume you have correctly determined the order in which the pirate labeled the trees as A, B, C, D, and E as shown in the figure. What are the coordinates of the point where his treasure is buried? (b) What If? What if you do not really know the way the pirate labeled the trees? What would happen to the answer if you rearranged the order of the trees, for instance, to B (30 m, 20 m), A (60 m, 80 m), E (10 m, 10 m), C (40 m, 30 m), and D (70 m, 60 m)? State reasoning to show that the answer does not depend on the order in which the trees are labeled. Figure 1.69
- If , and , find the unknown constants a and b such that .The velocity of a rocket is given as a function of time by v(t) = A(1 – e-bt) for 0 , t , 30 s, where the constants A = 150 and b = -0.15. [ d/dx (e-ax dx) = -a e-ax; ∫ e-ax dx = -1/a e-ax ] a) What are the SI units of A and b? b) What is the speed of the rocket at t = 10 s? c)Find the displacement of the rocket in the first 10 s ( from t = 0 s to t = 10 s)Newton’s law of universal gravitation is represented byF = G Mm r 2where F is the gravitational force, M and m are masses, and r is a length. Force has the SI units kg · m/s 2 . What are the SI units of the proportionality constant G?
- The acceleration of a particle is a constant. At t=0 the velocity of the particle is (14.91 + 18.4ĵ) m/s. At t = 4.6 s the velocity is 11.4j m/s. (Use the following as necessary: t. Do not include units in your answers.) (a) What is the particle's acceleration (in m/s²)? = î+ 18.4 v(t) = (b) How do the position (in m) and velocity (in m/s) vary with time? Assume the particle is initially at the origin. r(t) = î+ X Î- i) m/s m/sA graph of x vs. t4, with x on the vertical axis and t4 on the horizontal axis, is linear. Its slope is 31 m/s4 and its vertical-axis intercept is 8 m. Write an equation for x as a function of t. x = (31 m/s 4 )t 4 + 8 m x = (8 m )t 4 − 31 m/s 4 x=(31 m/s48 m)t4x=31 m/s48 mt4 x = (8 m )t 4 + 31 m/s 4The function f(t)=7600(1.85)^((t)/(7)) represents the change in a quantity over t days. What does the constant 1.85 reveal about the rate of change of the quantity?
- A stone is tossed into the air from ground level with an initial velocity of 30 m/s. Its height at time t is h(t) : 30t – 4.9t2 m. Compute the stone's average velocity ū in m/s over the time intervals [2, 2.01], [2,2.001], [2,2.0001] and [1.9999, 2], [1.999, 2], [1.99, 2]. (Use decimal notation. Give your answers to three decimal places.) Ū12,2.01] = m/s Ü12,2.001] = m/s U12,2.0001] = m/sA person sitting on a Ferris wheel rises and falls as the wheel turns. Suppose that the person's height above ground is described by the following function. h(t)=19.8+18.5 sin 1.9t In this equation, h (t) is the height above ground in meters, and t is the time in minutes. Find the following. If necessary, round to the nearest hundredth. Minimum height above the ground: meters Period of h: minutes Frequency of h: revolutions per minuteUse dimensional analysis to determine how the period T of a swinging pendulum (the elapsed time for a complete cycle of motion) depends on some, or all, of these properties: the length L of the pendulum, the mass m of the pendulum bob, and the gravitational field strength g (in m/s2). Assume that the amplitude of the swing (the maximum angle that the string makes with the vertical) has no effect on the period.
