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Motion in 2d or 3d

In physics, a vector is a quantity that has magnitude and direction. A vector can be understood as an arrow in space, whose magnitude is its length and whose direction points in the direction of its length. The magnitude of a vector is defined as its length, and the direction of a vector is the direction that its length points in space. If a vector has zero magnitude, it is said to be perpendicular to itself. A more elaborate example of a vector is where a particular vector has components along the three axes of a Cartesian coordinate system. The components are usually called "x", "y", and "z". This is called a "vector quantity". If it is a vector in the direction of the x-axis, for example, then it is usually called "x", if it is a vector along the y-axis, it is usually called "y", and if it is along the z-axis, it is usually called "z". In three dimensions, a vector quantity has components for the three axes of the three dimensional Cartesian coordinate system. In SI units, a vector quantity has an "m" component along each of the three axes, for a total of six components, and "N" components perpendicular to each of the three axes (i.e. perpendicular to the three Cartesian coordinate system axes). In Imperial units, the components are designated "x", "y" and "z". In mathematics, a vector quantity is an object that has both magnitude and direction. We would like to be able to define a vector quantity in such a way that we can add vectors and multiply them by scalars, just as we can add and multiply scalars. In particular, we can define a vector quantity as a function of a scalar and a direction. A vector quantity, in this sense, is a function. Just as a function of two variables may be defined by three equations, so a function of three variables may be defined by six equations. Often the two axes are called "x" and "y", and the third axis is called "z". Vectors that have magnitudes and directions (i.e., their components) are called "n"-vectors, while vectors that can be added to form a new vector are called "n"-tuple vectors. The concept of a vector is of fundamental importance in physics, as well as in many other branches of mathematics, engineering and the physical sciences. Vectors form the basis of vector calculus, which is the mathematical foundation for much of applied mathematics, physics, and engineering. Many geometric and physical properties are scalar properties, but when they are described at an appropriate level of detail, become vector quantities.

Position and Velocity Vectors

214 Practice Problems
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03:31
Engineering Mechanics: Statics and Dynamics

A particle is moving along a straight line such that its acceleration is defined as $a=(-2 v) \mathrm{m} / \mathrm{s}^{2},$ where $v$ is in meters per second. If $v=20 \mathrm{m} / \mathrm{s}$ when $s=0$ and $t=0$ determine the particle's position, velocity, and acceleration as functions of time.

Kinematics of a Particle
Zulfiqar Ali
03:01
Engineering Mechanics: Statics and Dynamics

A particle is moving with a velocity of $v_{0}$ when $s=0$ and $t=0 .$ If it is subjected to a deceleration of $a=-k v^{3}$ where $k$ is a constant, determine its velocity and position as functions of time.

Kinematics of a Particle
Hariprasad Annamalai
01:33
Engineering Mechanics: Statics and Dynamics

A particle travels along a straight-line path such that in 4 s it moves from an initial position $s_{A}=-8 \mathrm{m}$ to a position $s_{B}=+3 \mathrm{m} .$ Then in another $5 \mathrm{s}$ it moves from $s_{B}$ to $s_{C}=-6 \mathrm{m} .$ Determine the particle's average velocity and average specd during the 9 -s time interval.

Kinematics of a Particle
Zulfiqar Ali

The Acceleration Vector

37 Practice Problems
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04:06
College Physics

A powerful motorcycle can produce an acceleration of $3.50 \mathrm{m} / \mathrm{s}^{2}$ while traveling at $90.0 \mathrm{km} / \mathrm{h} .$ At that speed the forces resisting motion, including friction and air resistance, total 400 N. (Air resistance is analogous to air friction. It always opposes the motion of an object.) What is the magnitude of the force the motorcycle exerts backward on the ground to produce its acceleration if the mass of the motorcycle with rider is $245 \mathrm{kg} ?$

Dynamics: Force and Newton's Laws of Motion
Coleen Amado
01:58
College Physics

The same rocket sled drawn in Figure 4.30 is decelerated at a rate of $196 \mathrm{m} / \mathrm{s}^{2}$. What force is necessary to produce this deceleration? Assume that the rockets are off. The mass of the system is $2100 \mathrm{kg}$.

Dynamics: Force and Newton's Laws of Motion
Coleen Amado
01:55
College Physics

A cleaner pushes a 4.50-kg laundry cart in such a way that the net external force on it is $60.0 \mathrm{N}$. Calculate the magnitude of its acceleration.

Dynamics: Force and Newton's Laws of Motion
Coleen Amado

Projectile Motion

157 Practice Problems
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07:03
Principles of Physics a Calculus Based Text

Review. One side of the roof of a house slopes up at $37.0^{\circ} .$ A roofer kicks a round, flat rock that has been thrown onto the roof by a neighborhood child. The rock slides straight up the incline with an initial speed of $15.0 \mathrm{m} / \mathrm{s}$. The coefficient of kinetic friction between the rock and the roof is 0.400 . The rock slides $10.0 \mathrm{m}$ up the roof to its peak. It crosses the ridge and goes into free fall, following a parabolic trajectory above the far side of the roof, with negligible air resistance. Determine the maximum height the rock reaches above the point where it was kicked.

More Applications of Newton's Laws
Vishal Gupta
02:40
University Physics Volume 1

A rock is thrown straight up. At the top of the trajectory, the velocity is momentarily zero. Does this imply that the force acting on the object is zero? Explain your answer.

Newton's Laws of Motion
Linda Winkler
01:04
University Physics Volume 1

Answer the following questions for projectile motion on level ground assuming negligible air resistance, with the initial angle being neither $0^{\circ}$ nor $90^{\circ}:$ (a) Is the acceleration ever zero? (b) Is the vector v ever parallel or antiparallel to the vector a? (c) Is the vector v ever perpendicular to the vector a? If so, where is this located?

Motion in Two and Three Dimensions
Suzanne W.

Motion in a Circle

150 Practice Problems
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02:37
21st Century Astronomy

Electra is a 182 -km-diameter asteroid accompanied by a small moon orbiting at a distance of $1,350 \mathrm{km}$ in a circular orbit with
a period of 3.92 days.
a. What is the mass of Electra?
b. What is Electra's density?

Dwarf Planets and Small Solar System Bodies
Zachary Warner
02:00
21st Century Astronomy

Earth's Moon has a diameter of $3,474 \mathrm{km}$ and orbits at an average distance of $384,400 \mathrm{km}$. At this distance. it subtends an angle just slightly larger than half a degree in Earth's sky. Pluto's moon Charon has a diameter of $1,186 \mathrm{km}$ and orbits at a distance of $19,600 \mathrm{km}$ from the dwarf planet.
a. Compare the appearance of Charon in Pluto's skies with the Moon in Earth's skies.
b. Describe where in the sky Charon would appear as seen from various locations on Pluto.

Dwarf Planets and Small Solar System Bodies
Zachary Warner
01:20
21st Century Astronomy

An object in a(n) ________ orbit in the Solar System will remain in its orbit forever. An object in a(n) _______ orbit will escape from the Solar System.
a. unbound; bound
b. circular; elliptical
c. bound; unbound
d. elliptical; circular

Gravity and Orbits
Sarah Mccrumb

Relative Velocity

138 Practice Problems
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05:10
21st Century Astronomy

An astronomer sees a redshift in the spectrum of an object. Without any other information, can she determine whether this is an extremely dense object (exhibiting gravitational redshift) or one that is receding from her (exhibiting Doppler redshift)? Explain your answer.

Relativity and Black Holes
Sarah Mccrumb
03:21
21st Century Astronomy

During the period of inflation, the universe may have briefly expanded at $10^{30}$ (a million trillion trillion) or more times the speed of light. Why did this ultra-rapid expansion not violate Einstein's special theory of relativity, which says that neither matter nor communication can travel faster than the speed of light?

Cosmology
Sarah Mccrumb
01:00
21st Century Astronomy

If two spaceships approach each other, each traveling at $0.5 c$ relative to an outside observer, spaceship 1 will measure spaceship 2 to be traveling
a. much faster than $c$
b. slightly faster than $c$
c. at $c$
d. more slowly than $c$.

Relativity and Black Holes
Sarah Mccrumb

Position, Velocity, and Acceleration Vectors

186 Practice Problems
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04:28
Engineering Mechanics: Statics and Dynamics

The acceleration of a particle along a straight line is defined by $a=(2 t-9) \mathrm{m} / \mathrm{s}^{2},$ where $t$ is in seconds. At $t=0, s=1 \mathrm{m}$ and $v=10 \mathrm{m} / \mathrm{s} .$ When $t=9 \mathrm{s},$ determine
(a) the particle's position,
(b) the total distance traveled, and (c) the velocity.

Kinematics of a Particle
Hariprasad Annamalai
03:58
Engineering Mechanics: Statics and Dynamics

The position of a particle along a straight line is given by $s=\left(1.5 t^{3}-13.5 t^{2}+22.5 t\right) \mathrm{ft},$ where $t$ is in scconds. Determine the position of the particle when $t=6$ s and the total distance it travels during the 6 -s time interval. Hint: Plot the path to determine the total distance traveled.

Kinematics of a Particle
Zulfiqar Ali
06:33
Engineering Mechanics: Statics and Dynamics

The velocity of a particle traveling in a straight line is given by $v=\left(6 t-3 t^{2}\right) \mathrm{m} / \mathrm{s},$ where $t$ is in seconds. If $s=0$ when $t=0,$ determine the particle's deceleration and position when $t=3$ s. How far has the particle traveled during the 3 -s time interval, and what is its average speed?

Kinematics of a Particle
Zulfiqar Ali

Two-Dimensional Motion with Constant Acceleration

47 Practice Problems
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03:22
Physics for Scientist and Engineers A Strategic Approach

Problems 1 through 3 show a partial motion diagram. For each:
a. Complete the motion diagram by adding acceleration vectors.
b. Write a physics problem for which this is the correct motion diagram. Be imaginative! Don't forget to include enough information to make the problem complete and to state clearly what is to be found.
(FIGURE CANNOT COPY)

Kinematics in Two Dimensions
Lisa Tarman
01:58
College Physics

The maximum height of the ball will be
A. the same as on earth
B. higher
C. lower

Motion in a Plane
Jayashree Behera
02:32
College Physics

The ball will stay aloft
A. the same amount of time as on the earth
B. a shorter amount of time
C. a longer amount of time

Motion in a Plane
Averell Hause

Tangential and Radial Acceleration

68 Practice Problems
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01:08
21st Century Astronomy

The spectroscopic radial velocity method preferentially detects
a. large planets close to the central star
b. small planets close to the central star.
c. large planets far from the central star.
d. small planets far from the central star.
e. the method detects all of these equally well

The Birth and Evolution of Planetary Systems
Sarah Mccrumb
03:43
Principles of Physics a Calculus Based Text

A wheel $2.00 \mathrm{m}$ in diameter lies in a vertical plane and rotates about its central axis with a constant angular acceleration of $4.00 \mathrm{rad} / \mathrm{s}^{2} .$ The wheel starts at rest at $t=0,$ and the radius vector of a certain point $P$ on the rim makes an angle of $57.3^{\circ}$ with the horizontal at this time. At $t=2.00 \mathrm{s}$ find (a) the angular speed of the wheel and, for point $P$
(b) the tangential speed, (c) the total acceleration, and
(d) the angular position.

Rotational Motion
Rehmat Kazmi
02:25
University Physics Volume 1

Suppose a piece of food is on the edge of a rotating microwave oven plate. Does it experience nonzero tangential acceleration, centripetal acceleration, or both when: (a) the plate starts to spin faster? (b) The plate rotates at constant angular velocity? (c) The plate slows to a halt?

Fixed-Axis Rotation
Griffin Goodwin

Relative Velocity and Relative Acceleration

22 Practice Problems
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00:26
University Physics

Which of Einstein's postulates of special relativity includes a concept that does not fit with the ideas of classical physics? Explain.

Relativity
Dading Chen
02:36
Essential University Physics

The Global Positioning System (GPS) uses a "constellation" of some 30 satellites to provide accurate positioning for any point on Earth (Fig. 8.19 ). GPS receivers time radio signals traveling at the speed of light from three of the satellites to find the receiver's position. Signals from one or more additional satellites provide corrections, eliminating the need for high-accuracy clocks in individual GPS receivers. GPS satellites are in circular orbits at $20.200 \mathrm{km}$ altitude.
(FIGURE CAN'T COPY)
What's the approximate speed of GPS satellites?
a. $9.8 \mathrm{m} / \mathrm{s}$
b. $500 \mathrm{m} / \mathrm{s}$
c. $1.7 \mathrm{km} / \mathrm{s}$
d. $4 \mathrm{km} / \mathrm{s}$
e. $12 \mathrm{km} / \mathrm{s}$

Gravity
Donald Albin
02:27
Physics

An object has a relativistic momentum that is 8.50 times greater
than its classical momentum. What is its speed?

Relativity
João Gabriel Alencar Caribé

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