### Distance, Velocity and Time: Equations and Relationship | Science project | ogloszenia-praca.info

Home» Applications of Integration» Distance, Velocity, Acceleration that will later be applied to distance-velocity-acceleration problems, among other things. Jun 10, Time is the medium for both velocity and acceleration to occur. distance- This distance is defined by the velocity or acceleration. Another relationship between the two is that when velocity is constant, acceleration is zero. May 4, Learning the constant acceleration equations sets you up perfectly for this type of problem, and if you have to find acceleration but only have a.

Make sure to make your graph large so you have room to expand it if necessary! On the Y axis, mark the distance in centimeters from zero to centimeters. Remember— centimeters is the same as 1. Plot the velocity of the slower car. Your first point should be at 0,20 cm because you are going to give it a cm head start.

Your second point for the slow car is the velocity you measured. The X value should be whatever time it took for the car to reach the end of your test course, your Y value is the distance you had the car travel 1. Using your ruler and pencil, connect the two points to make a line. Now, plot the velocity of the faster car. Your first point should be at 0,0 cm because this car will not get a head start.

Your second point for the fast car is the velocity you measured. Using your ruler and pencil connect the two points to make another line. Make this line look different than the first, either by making dashes or making it darker. Label the lines fast car and slow car. Find where the two lines cross.

### Distance, Velocity, and Acceleration

At this intersection point, trace one line to X axis, and another to the Y axis. These are the lines with arrows on diagram 1. The two values you see are the time and distance where the fast car should overtake the slower car. Mark the predicting passing point on your course. Mark off the calculated point where the faster car should overtake the slower car.

Have your assistant release the slower car at the head start mark while you simultaneously release your faster car at the starting line. Start the timer a third person might be nice for this. Watch carefully to see where the fast car overtakes the slow car. And, by Newton's 2nd Law, this must be equal to the mass times the x-component of the acceleration since mass has no direction, and acceleration is also a vector.

Similarly as above, if I have a series of forces acting on a mass, the sum of their y-components must be equal to the y-component of the net force on the mass. And, by Newton's 2nd Law, this must be equal to the mass times the y-component of the acceleration since mass has no direction, and acceleration is also a vector. If we calculate or just know the x- and y-components of the net force acting on an object, it is a snap to find the total net force. As with any vector, it is merely the sum of its components added together like a right triangle, of course.

This equation becomes ridiculously easy to use if either one of the components is zero.

### How are acceleration, time and velocity related? | Socratic

The definition of momentum is simply mass times velocity. Take note that an object can have different velocities measured from different reference frames. Newton's 2nd Law re-written as an expression of momentum change. This is actually how Newton first thought of his law.

It allows us to think of momentum change as "impulse" force over some timeand apply the law in a much simpler fashion. In a closed, isolated system, the total momentum of all the objects does not change. Since "closed" means nothing coming in or going out, we can imagine all our applications talking about a fixed set of objects.

Since "isolated" means no interactions with anything outside the system, we must imagine all our applications involve nothing but those objects and forces that we consider.

In two dimensions, the law still holds -- we just pay attention to the components of the total momentum. Here, a' refers to object a after the collision. This equation shows the relationship between arclength sradius rand angle theta - measured in radians. It is useful for finding the distance around any circular path or portion thereof at a given radial distance. This equation shows the relationship between the period of a pendulum and its length. It was first discovered by Galileo that the arc of a pendulums swing and the mass at the end of a pendulum do not factor noticeably into the amount of time each swing takes.

Only the length of the pendulum matters.

The tangential velocity of an object in uniform unchanging circular motion is how fast it is moving tangent to the circle. Literally the distance around the circle divided by the period of rotation time for one full rotation. The centripetal acceleration of an object in uniform circular motion is how much its velocity because of direction, not speed changes toward the center of the circle in order for it to continue moving in a circle. The force that is required to keep an object moving in a circular path is the centripetal force acting on the object.

This force, directed towards the center of the circle, is really just a derivative of Newton's 2nd Law using centripetal acceleration. The work done on an object is found by multiplying force and distance, but there is a catch.

The force and distance must be parallel to each other. Only the component of the force in the same direction as the distance traveled does any work. Hence, if a force applied is perpendicular to the distance traveled, no work is done.

The equation becomes force times distance times the cosine of the angle between them.

Work is measured in units of newtons times meters, or joules J. Power is a physical quantity equal to the rate at which work is done. The more time it takes to do the same work, the smaller the power generated, and vice-versa. Power is measured in units of joules per second, or watts W.

Kinetic energy is simply the energy of motion - the more something is moving or the more there is to that somethingthe more kinetic energy it possesses. Kinetic energy, like all forms of energy, is measured in units of joules J. Since work and energy have the same units, it stands to reason that they are related. Energy is really defined as the ability to do mechanical work. Therefore, if positive work is done on an object, that object gains kinetic energy it gets moved.

This is just a different version of the above equation. It is commonly referred to as the Work-Energy Theorem.

Gravity is a constant force - always there and always the same. Since this is the case, we can say that as an object gains height near the surface of the Earthit gains some potential to do work when it eventually falls. This potential energy is stored energy that can be turned into kinetic later. The total mechanical motion-related energy of an object is found by adding the kinetic plus the potential energies for that object - energy due to how fast it is currently going and due to how fast it could go because of its position.

This is a simplified mathematical re-statement of the law of energy conservation. If we have a closed and isolated system, the total mechanical energy does not change.

## Distance, Velocity, and Acceleration

This is the definition that links the relationship between frequency measured in Hz -- or cycles per second and period measured in units of time -- seconds per cycle.

The inverse relationship between the two is important in relating wave speed with wavelength. The speed of a wave is due to only two features, the frequency of the wave pattern and the wavelength how far apart the waves are in space.

It is important to note that there is no dependence on the amplitude of the wave for calculating the frequency.

The energy carried by a wave is proportional to the square of the amplitude of the wave and has nothing to do with wave speed. Therefore, if I were to double the amplitude of a wave like doubling the intensity of a sound I am actually quadrupling the energy that it carries.

This equation shows the relationship between three variables of a string attached at two ends and the velocity of a transverse wave that would travel between them. The variable F is the tension force in the string; the variable m is the mass of the string; and the variable L is the length of the string. Therefore, in order to make a wave travel faster in a string like a guitar stringI can do any one of three things while keeping the others constant: Sound waves or any other form of three dimensional emanation can be ranked by their intensity -- an objective measure of the amount of energy they carry.

At some distance, r, from a point source of sound with power output, P, the intensity can be calculated in Watts per square-meter. This is a much more objective view of "loudness" than is measured by the decibel scale, in which the frequencies of the sound matter due to limitations on the human range of hearing 20 Hz to 20 kHz.

The Doppler Effect can be detected whenever a wave source and observer are in relative motion. If they are moving towards each other, then the frequency is observed to be higher than what is actually emitted, and vice versa.

Otherwise, the bottom sign is used in either case. The entire factor in parentheses is actually a unit-less quantity that acts as a multiplier for the emitted frequency, f. For either an open-ended resonator or a sting attached at both ends, this equation allows you to calculate the frequency of a standing wave with the integer, n, number of antinodes or loops.