Answered: How do you define and calculate the…

How do you define and calculate the velocity, speed, direction of motion, and acceleration of a body moving along a su¨ciently di¡erentiable space curve? Give an example.

Related questions

Q: velocity of the proton in units of km/s

A: Given: Mass of proton is m=1.673×10-27 kg Charge on proton is q=1.6×10-19 C Radius of path is r=4.46…

Q: If the Earth had twice the radius but the same density (assume constant density), then the…

Q: A typical neutron star may have a mass equal to that of the Sun but a radius of only 19 km. (a) What…

A: radius = 19 km mass of neutron star = mass of sun mass of neutron star = 1.99×1030 kg

Q: The Sun, which is 2.2 * 10^20 m from the centerof the Milky Way galaxy, revolves around that center…

A: Thus,

Q: While a balloon-supported gondola is rising at a speed of 2.0 m/s, a passenger in the gondola throws…

A: Given Velocity of gondola w.r.t ground VgG = 2.0 m/s ............ upward Velocity of…

Q: The Orion Space Capsule has started it's return to earth and is travelling at a speed of 24,600 mph.…

A: Given data, Speed=24600 mph Distance d=270,000 miles

Q: The Small Magellanic Cloud is a dwarf galary orbiting the Milky Way at a distance of 50 kiloparsecs…

A: Given: The observed velocity of the Small Magellanic cloud relative to the Milky way is v = 207 km/s…

Q: a) A 95 kg astronaut stands on the surface of a spherical asteroid with a mass of 4.5 x 1015 kg and…

A: Please see the answer below.

Q: Determine the fundamental dimensions[e.g. L (length), T (time) etc.] of the universal gravitation…

A: The gravitational force between the two objects is written as, Here, G, m1, m2 and d represent the…

Q: Taking the age of Earth to be about 4 ✕ 109 years and assuming its orbital radius of 1.5 ✕ 1011 m…

Q: The speeds of John and Max are 30 km/h and 40 km/h. Initially Max is at a place L and John is at a…

Q: Suppose it is known that the earth attracts an object with a force that decreases at the rate of 2…

Q: You are traveling in a car going at a constant speed of 100 km/hr down a long, straight highway. You…

A: In the above question the car is moving back and forth with the constant velocity. As the velocity…

Q: The gravitational force exerted by the planet Earth on a unit mass at a distancer from the center of…

Q: Inertial observers experience no acceleration. What is a simple experiment that a moving observer…

A: in this type of question find what is inertial references and give example of it and then discuss…

Q: SB.5 An event occurs at t = 6.0 s and x = 4.0 s in the Home Frame. The Other Frame is moving in the…

Q: A star is pulsating isotropic ally. Its gravitational fore on any body, at distances much larger…

A: ans ;- option (a)

Q: A new satellite launched to the space. It is orbiting the earth so that its displacement f north of…

A: From the expression of the displacement function, it can be seen that f is a periodic function. f=A…

Q: An object of mass mm is launched from a planet of mass MM and radius RR. a) Derive and enter an…

Q: You might have had the experience of being at a red lightwhen, out of the corner of your eye, you…

A: Absolute motion refers to the motion of an object in a stationary frame of reference. Relative…

Q: A probe of mass 100 kg is coasting through a dense gas cloud in deep space, where g = 0. There is…

A: Using Newton’s second law of motion mdvdt=Fdmdvdt=-0.6v∫vivfdvv=∫-0.6mdtlnvfvi=-0.6tm

Q: You have negotiated with the Omicronians for a base on the planet Omicron Persei 7. The architects…

Q: o What LineaN speed must an Earth Satellite have to be in ciNculay Oxbit at an altitude of 182 Km…

A: The altitude of the satellite in earth orbit is given as h = 182km.

Q: Two particles move about each other in circular orbits under the influ- ence of gravitational…

Q: Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets…

A: Given : Mass of Venus, MV = 0.815 ME Mass of Jupiter, MJ = 318 ME Mass of Saturn,…

Q: Goku's birthplace (in Dragon Ball Z universe) is planet Vegeta which has a really high surface…

A: If Goku launced himself with same initial velocity, it means kinetic energy is same for both launch.

Q: At what rate must a cylindrical spaceship rotate if occupants are to experience simulated gravity of…

Q: Trixie and Katya Consider a Newtonian universe with only two observers, Trixie and Katya. Which of…

A: A Newtonian universe is one in which all of Newton's laws are valid. The position and motion of a…

Q: Captain James T. Kirk of Star Trek fame spent a large portion of his time mining for planets that…

A: The radius of the planet=rThe period of the orbit=TMass of ship=mThe minimum distance of his ship…

Q: The radius Rh of a black hole is the radius of a mathematical sphere, called the event horizon, that…

A: Given, Rh = 2GM/c2 a. Gravitational acceleration is given byag=Gmr2dag=2Gmr3drSince, h<<48…

Q: You fire a light signal at 60° north of west. (a) Find the velocity components of this signal…

A: Light is fired at 60° N of W A) observer moving Eastwards B) observer moving Westwards

Q: 2) If it takes +1.6×10-5 J to move a positively charged particle between two charged parallel…

A: The work done to move a positive charge q from the negative plate (lower potential) to the positive…

Q: Three uniform spheres of masses m1 = 2.50 kg, m2 = 4.00 kg, and m3 = 7.50 kg are placed at the…

A: Given Datam1 = 2.5 kgm2 = 4 kgm3 = 7.5 kgDistance between m1 and m2, r12 = 3 mDistance between m3…

Q: In our inertial reference frame, we see a particle accelerating with a velocity dx/dt = ( 1 -…

Q: A rifle that shoots bullets with a muzzle speed of 1461 m/s is aimed at a target 807.0 m away. If…

Q: An ideal superball clock features a ball bouncing back and forth between two walls in gravity-free…

Q: Wonder Woman and Superman fly to an altitude of 1630 km,1630 km, carrying between them a chest full…

A: The chest is dropped from a height h=1630 km and since it is dropped the initial velocity u=0. The…

Q: When we seprate two members of a frame, we must represent the internal forces. Internal forces at…

A: According to Newton's Third law of motion: If a force is applied to an object by a person, the…

Q: 3-1. A free particle is moving in an inertial frame (x, y, z) in the xy -plane on a trajectory = d,…

Q: Consider the equation for kinetic energy: KE = 1/2mv^2 = 1/2 * m * v^2. If I ask you to take the…

Q: Mars orbits the Sun in a nearly circular orbit of radius 2.28 × 10" m. The mass of Mars is 6.42 x…

Q: An astronomer on Earth observes red light at 680 nm from a distant galaxy. The astronomy knows that…

A: In this case, the astronomer on earth observed red light from a galaxy. The wavelength of the red…

Q: 8. Two stars a and 3, with masses satisfying ma/m3 = 10, are in circular orbits around each other.…

A: Have a look dear

Q: In frame o an object moves in the x-direction with velocity u= 0.82c. Find the magnitude of the…

A: The object moving in frame o has velocity 0.82cThis is the inertial frame of the objectAnother frame…

Q: Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8 ✕ 1011…

Concept explainers

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

Question

How do you define and calculate the velocity, speed, direction of motion, and acceleration of a body moving along a su¨ciently di¡erentiable space curve? Give an example.

Expert Solution

Step 1

Velocity- It is define by rate of change in displacement with respect to time.It is represented by $v .$

$v = \frac{d r}{d t}$

Speed- The magnitude of $v$ is the particle called speed.It is define as

$S p e e d = |v|$

Direction of motion- If $v$ is a nonzero vector,then it's tangent to curve and it's direction is the direction of motion.it ia given by

$\hat{n} = \frac{v}{|v|}$

Acceleration- It is define as the rate of change of velocity with respect to time is given as

$a = \frac{d v}{d t} = \frac{d}{d t} (\frac{d r}{d t}) = \frac{d^{2} r}{d t^{2}}$

Step by step

Solved in 2 steps

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-physics and related others by exploring similar questions and additional content below.