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# Velocity

Velocity is the rate of change of the position of an object. It is equivalent to the speed and direct of motion. Speed is a scalar quantity whereas velocity is a vector quantity. Velocity gives the magnitude and direction of motion. For example, if a car is moving at 100 km/h to the west, the velocity has been specified. If the velocity is constant, the object has a constant speed in a constant direction.

There are many equations of motion to calculate velocity.

v= Δx/Δt (1)

v=u+aΔt (2)

v^2= u^2+2aΔx (3)

Velocity can also be two-dimensional and expressed in polar coordinates. With polar coordinates, there are two types of velocity, radial and angular velocity. Radial velocity is the component of velocity away from or towards the origin. The angular velocity is the rate of rotation about the origin. The transverse velocity is the component of velocity along ta circle centered at the origin. The equation of velocity in a polar coordinate system is:

v=v_T+ v_R (4)

The magnitude of the radial velocity is a dot product. The equation is as followed:

v_R= (v*r )/(|r|) (5)

Where r is the displacement.

## Categories within Velocity

### Determining Initial Velocity

In a baseball game a base-runner can attempt to advance when a fielder catches a hit ball before it reaches the ground, so long as the runner doesn't leave base before the fielder catches the ball. The fielder then attempts to throw the ball to the base ahead of the runner. If a base-runner can run from 3rd base to home plate in

### Finding the moment of inertia

A sheet of plywood 1.37 cm thick is used to make a cabinet door 50.9 cm wide by 76.9 cm tall, with hinges mounted on the vertical edge. A small 191-g handle is mounted 45 cm from the lower hinge at the same height as that hinge. If the density of the plywood is 550 kg/m^3, what is the moment of inertia of the door about the hing

### Physics Problems: Velocity, Impact, Speed

a) Mr. Stick lives on the planet Teflon where the force due to gravity is different than that of Earth. Mr. Stick drops a small water balloon off the top of a building (V0 = 0 m/s). He releases the balloon at a height H = 10 m above the surface of Teflon. The balloon hits the ground 1.8 seconds after it is dropped and has a velo

### Modelling Projectile Motion Problem

Modelling problem - Plan the solution by set up equations and - Execute & Evaluate = do the problem, state the answer & INCLUDE UNITS!!! A football is kicked across a level field. The ball spends 3 seconds in the air and lands 60 m from the point where it was kicked. (Ignore air resistance). a) What is the speed of the

### Formula for Final Velocity

How would I rewrite the formula for initial velocity to solve for final velocity vf. I didn't know how to write the dot in the middle meaning to multiple in the equation (a.t) it means (a X t) see below: vi=vf-(a.t)

### Finding Minimum Launch Velocity

The velocity v of a rocket attempting to escape from the earth's gravitational field is given by: (v)(dv/dr) = -g(R^2/r^2) Where: r is its distance from the centre of the earth and R is the mean radius of the earth Find a formula for V(r) and determine the minimum launch velocity V0 in order that the rocket escap

### Average Power Output & Group Velocity

(b) A tidal basin in Canada has an area of 240 km^2 with a mean tidal range of 12.4 m. Estimate the average power output assuming that the tidal period is 12.5 hours explaining your calculation. (c) An ocean wave, with amplitude a = 1m and wavelength...(Please see the attached file for the complete question.)

### Finding Overall Speed and Velocity

Each of parts (b), (c) and (d) requires you to use numerical answers found in earlier parts of the question. A dragonfly has a flight speed in still air of 4.5ms-1. It is pointed in the direction N - 29 degree - E, but flies in a wind of speed 7.5ms-1 from the direction S- 42 degree - E. Take i to be 1ms-1 due east and j to

### Summary of kinematics, solutions to kinematics problems.

Here, we provide a brief summary of some common kinematics, and solve three common kinematics problems, specifically from College Physics, by J. Serway, et al. We specifically find: For a car traveling east at a given velocity, the final velocity for a constant acceleration in two different directions. For an arrow shot s

### Group velocity of localized waves

Section 2-2 discusses the superposition of two classical sinusoidal waves of slightly different wave numbers k and k+[delta]k to yield a modulated result whose modulations move with a group velocity. A composition almost as simple as the two-component case is the superposition of three waves y_0, y_1, and y_2 with the same tota

### Speed and Momentum Calculations

A pitcher claims he can throw a 0.168 kg baseball with as much momentum as a 3.32 g bullet moving with a speed of 1.21584x10^5 m/s. What must be its speed if the pitcher's claim is valid? Answer in units of m/s. This is an "explosion" question. A 30-06 caliber hunting rifle fires a bullet of mass 0.0115 kg with a velocity of

### Physics Practice Test: Tension, Acceleration, Velocity Etc.

See the attached file. 1. A plane leaves the airport and flies east at 109 miles/hour. 4.5 hour(s) later a second plane leaves east at 240 miles/hour. How long after taking off does the second plane overtake the first plane? 2. What is the tension on an elevator cable if the elevator (with a mass of 1209.3 kg) is traveling

### Velocity Algorithm Code

Write the simplest possible one-dimensional "molecular dynamics code" for two particles. I used matlab, so i need matlab code for molecular dynamics or velocity verlet algorithm code. I need to determine x1, x2 and v1, v2 in different time steps. I have the following 15 values for x1, x2 and v1,v2 in graphs: M = 1.0 d

### Cannon Ball Trajectory

A canon ball with mass m has a mechanism that blows it into 4 pieces of equal mass, who spread (relative to the canon ball with no motion) at 90 angles: forward, backwards, down, up in equal velocities. The canon ball is being fired from a canon at velocity V and angle of 45 degrees above the horizon, and it spreads at the ma

### Molecular Dynamics MATLAB Code

Write the simplest possible one-dimensional "molecular dynamics code" for two particles? I use MATLAB, so I want a MATLAB code for molecular dynamics or velocity verlet algorithm code. I need to determinate x1, x2 and v1, v2 in different times. Some websites may help you: [http://www.nada.kth.se/~tomaso/miklab2007/lab2_4h

### Determining Time, Distance and Velocity

1. A shuffle board table is 5 feet tall. A puck slides off the table at 2 m/s. How how long does it take to hit the ground? 2. A shuffle board table is 5 feet tall. A puck slides off the table at 2 m/s. How far across the room does it travel in 1 second? 3. An apple weighs 2 KG. The earth exerts a force of 20 Newtons on th

### Force by the ground on the tennis ball

A tennis ball of mass 0.06 kg is served. It strikes the ground with a velocity of 54 m/s at an angle of 22 degrees below the horizontal. Just after the bounce it is moving at 53 m/s at an angle of 19 degrees above the horizontal. If the interaction with the ground lasts 0.067 s, what average force did the ground exert on the bal

### Velocity, Highest Point, and Maximum Height

1. A ball is thrown vertically upward with a speed of 23.3 m/s. a) How long does it take to reach its highest point? b) What is its velocity when it returns to the level from which it started? 2. A ball thrown vertically upward is caught by the thrower after 2.9 s. The acceleration of gravity is 9.8 m/s a) Find

### Vectors and Velocity Problem

I need a perfect step by step solution of the following problem: A particle of charge q is started at the origin with an initial velocity (vector)v_0 = v_0 x(^), in a region where a uniform electric field exists (vector)E = E_0 z(^), and a magnetic field intensity is given by (vector)B = B_0 x(^) + B_0 y(^). HINT: ROTATE TH

### Translational Velocity

An object of your choice, of radius R, is given an initial angular velocity about a horizontal axis of w_0 (omega(initial)). The object is then set down on a surface that has a friction coefficient of u and released. What is the translational velocity of the object as it rolls away from the initial point of contact?

### Angular velocity and time

A person with a 50cm ponytail is using a lathe which is turning at 300rpm. The person turns their head, catching the end of the ponytail in the work piece, which has a diameter of 7cm. How long will it take the person's head to be dragged into the lathe?

### Velocity of Water Fountain

Suppose the water fountain rises vertically to 150 ft above the lake (when operated). Neglecting wind effects and minor losses, determine the velocity at which the water is ejected. See figure attached.

### Using the Difference Quotient to Calculate Average Velocity

A ball is released at the top of a ramp (an inclined plane). The distance it travels can be expressed as the function: s(t)=5t^2, where t is the time in seconds after the ball is released. The distance function, s(t), is measured in feet. Find the average velocity of the ball for the time interval [1,4].

### Kinematics and Dynamics Question: Speed

A ball is released from top of 98 m tall building. At the same instant a second ball is thrown straight up from the ground with an initial speed of 28 m/s directly below the point where the first ball was dropped. Ignore air resistance. a. At what height above the ground do the balls collide? b. What are the balls velociti

### Bernoulli's Principles: Static Water Pressure Problem

The static water pressure at point 1 in a pipe is 100 kPa, and the fluid velocity is 2 m/s. At point 2 downstream, the pipe narrows and the velocity increases to 3 m/s. What is the static pressure at that point? The usual assumptions concerning laminar flow, no friction losses, incompressibility, etc. all apply. This is in refer

### Electromagnetism: Force on electron in magnetic field

If the magnetic induction is 10^-2 weber/m^2 in the x-direction, find the force on an electron whose velocity is 10^7 m/s in (a) the xy-plane at 45 degrees to the x-axis, (Answer: 1.13x10^-14 N in the z-direction) (b) a direction making equal angles with the three axes. (Answer: 1.31 x10^-14 N in the YZ-plane)

### Velocity of Elastic Collision

A 0.10-kg object with a velocity of 0.20 m/s in the +x direction makes a head-on elastic collision with a 0.15 kg object that is initially at rest. What is the final velocity of the 0.10 object after the collision? Please provide detailed explanation.

### Rock Thrown horizontally, with a velocity of 10 m/s, from a bridge

A girl throws a rock horizontally, with a velocity of 10 m/s, from a bridge. It falls 20 m to the water below. How far does the rock travel horizontally before striking the water?

### Water Flow

Water flows from a hole in a uniform cylinder whose cross-section is a circle of radius .2867 meters. The hole has a radius of .061 meters. Determine the velocity with which water exits the hole when the cylinder is filled to a point 4.9 meters above the hole. Do not assume that the water in the cylinder is stationary. Please

### Earth Science: Force and Motion

The file is attached as it have some diagrams.