Two particles A and B start from rest at the origin s = 0 and move along a straight line such that aA = (6t − 3) m/s^2 and aB = (12t2 − 8) m/s^2, where t is in seconds. Determine the distance between them and the total distance each has travelled at t = 4s.

If ů = (7,–6, 0) and i = (1, 1,0), find the length and direction of ủ x i and i x ū. Length of u x i is ... ... Direction of u xở is (If u X v does not have a direction, enter "none".) Length of i x ủ is Direction of ú xũ is (If i xủ does not have a direction, enter "none".)

A cylindrical spaceship of length 35.0 m and diameter 8.35 m is traveling in the direction of its cylindrical axis (length). It passes by the Earth at a relative speed of 2.44××1088 m/s. a) What is the length of the ship, as measured by an Earth observer? b) What is the diameter of the ship, as measured by an Earth observer? c) How long does it take the spaceship to travel a distance of 10.0 km according to the ship's pilot? d) How long does it take the spaceship to travel a distance of 10.0 km according to an Earth-based observer?

In certain physical models, the nonhomogeneous term, or forcing term, g(t) in the equation ay" + by' + cy = g(t) may not be continuous, but have a jump discontinuity. If this occurs, a reasonable solution can still be obtained using the following procedure. Consider the following initial value problem. 240 if 0sts7T/6 y" + 4y' + 40y = g(t); y(0) = 0, y'(0) = 0, where g(t) = . if t> 7x/6 Complete parts (a) through (c) below. (a) Find a solution to the initial value problem for 0 sts 71/6. The solution for 0sts 7n/6 is y(t) = - 6 e -21 *cos 6t - 2 e - 2t sin 6t + 6 (Type an equation.) (b) Find a general solution for t> 71/6. The general solution for t> 7x/6 is y(t) = C, e-2 cos 6t + C, e -2t sin 6t (Type an equation. Do not use d. D. e, E, i, or I as arbitrary constants since these letters already have defined meanings.) (c) Now choose the constants in the general solution from part (b) so that the solution from part (a) and the solution from part (b) agree, together with their first…

In the red shift of radiation from a distant galaxy, a certain radiation, known to have a wavelength of 434 nm when observed in the laboratory, has a wavelength of 462 nm. (a)What is the radial speed of the galaxy relative to Earth? (b) Is the galaxy approaching or receding from Earth?

Two infinitely-long conductors parallel to the z-axis pass through the points (0,±a).

Helpful information: (1) An alpha particle is a helium nucleus, (2) e = 1.6 × 10-¹⁹ C, (3) k₂ = 9.0 × 10⁹ Nm² C-2, (4) 1nm = 1 × 10-⁹ m 1-An alpha particle lies on the x-axis, a distance of 1.0 nanometer from a proton (in this set-up, the alpha particle is at the origin while the proton is in the positive direction). Which of the following choices below represents the magnitude of the electric force on the alpha particle? (a) 2.3 × 10-10 N (b) 4.6 × 10-10 N (c) 2.3 x 10-19 N (d) 4.6 x 10-19 N cing the voltage so following insta choices below at a time! 1.00 s?

Chapter 37, Problem 015 The center of our Milky Way galaxy is about 24000 ly away. (a) To eight significant figures, at what constant speed parameter would you need to travel exactly 24000 ly (measured in the Galaxy frame) in exactly 27 y (measured in your frame)? (b) Measured in your frame and in lightyears, what length of the Galaxy would pass by you during the trip? (a) Number Units (b) Number Units

What is the discrepancy (according to an observer on the surface of the Earth), due to the general relativistic (i.e. gravity-based) time dilation, between the clock on a particular communications satellite and a clock on the surface of the Earth after 1 day. Ignore the sign of the discrepancy. Orbital Radius of satellite = 4.0 x 10 m 6.37 x 106 m %3D Radius of the Earth = Mass of Earth = 5.97 x 1024 kg Gravitational Constant = 6.67 x 10-11m3 kg-1 s-2 Speed of light =3 x 108 m/s %3D

An ant crawls on the surface of a ball of radius b in such a manner that the ant's motion is given in spherical coordinates by the equations r = b; phi = omega*t; theta = pi/2 * [1 + 1/4 * cos(400t)] Find the speed of the ant as a function of the time t. What sort of path is represented? by the above equations ?