Monday, September 25, 2023

# How To Get The Distance In Physics

## What Is Lens Formula

How to Use a Kinematic Equation to Find Distance Traveled : Physics & Math

Lens formula is defined as the relationship between object distance , image-distance and the focal length . Following is the mathematical representation of lens formula:

 \

Where,

• f is the focal length of the lens
• v is the distance of the image from the optical centre of the lens
• u is the distance of an object from the optical centre of the lens

## How To Calculate Distance From Acceleration And Velocity

Contents

In this article, we will learn how to calculate distance from acceleration and velocity. We would consider a special case of motion where our object under consideration is moving with constant acceleration. Here in this article, we will only discuss the formula for calculating the distance from acceleration and velocity only. The formula we would be using does not involve time. However, if you are aware of initial and final velocity and acceleration you can find time using the first equation of motion which is $v=u+at$.

Before going any further we must be aware of all the terms used. So,

Distance:- Distance covered by a moving object refers to how much ground the object has covered without any regard to the direction of motion. SI unit for measuring distance is meter.

Velocity:- Distance traveled by the moving body per unit of time gives the measure of the velocity of the object. It tells about how far an object moves in a given interval of time. SI unit for measuring velocity is meter per second .

Acceleration:- Acceleration is the rate of change of velocity of an object with respect to time. Like velocity, it is a vector quantity having both magnitude and acceleration. Its unit is $m/s^2$

## How To Calculate Tension In Physics

In physics, tension is the force exerted by a rope, string, cable, or similar object on one or more objects. Anything pulled, hung, supported, or swung from a rope, string, cable, etc. is subject to the force of tension.XResearch source Like all forces, tension can accelerate objects or cause them to deform. Being able to calculate tension is an important skill not just for physics students but also for engineers and architects, who, to build safe buildings, must know whether the tension on a given rope or cable can withstand the strain caused by the weight of the object before yielding and breaking. See Step 1 to learn how to calculate tension in several physical systems.

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## Finding Distance With Average Speed And Time

• 1Find values for average speed and time. When you try to find the distance a moving object has traveled, two pieces of information are vital for making this calculation: its speed and the time that it has been moving.XResearch source With this information, it’s possible to find the distance the object has traveled using the formula d = savg × t.
• To better understand the process of using the distance formula, let’s solve an example problem in this section. Let’s say that we’re barreling down the road at 120 miles per hour and we want to know how far we will travel in half an hour. Using 120 mph as our value for average speed and 0.5 hours as our value for time, we’ll solve this problem in the next step.
• 2Multiply average speed by time. Once you know the average speed of a moving object and the time it’s been traveling, finding the distance it has traveled is relatively straightforward. Simply multiply these two quantities to find your answer.XResearch source
• Note, however, that if the units of time used in your average speed value are different than those used in your time value, you’ll need to convert one or the other so that they are compatible. For instance, if we have an average speed value that’s measured in km per hour and a time value that’s measured in minutes, you would need to divide the time value by 60 to convert it to hours.
• ## Can We Find Velocity Using The Force Formula Now when we first think about force the following force formula comes to our mind $$F=ma$$ This formula involves force, mass, and acceleration. Again from the acceleration formula with velocity and time, we know that $$a=\frac$$ where \ is the velocity of the moving object and $t$ is the time taken.To find the velocity of the particle using the force formula we must have knowledge about

• the force acting on the moving object and
• time for which force acts

Please note here that distance traveled does not figure in the equation $$v=\frac$$. So we can not use the force formula to find the velocity of the object from force and distance.

## Subsectionwhen Velocity Is Negative

The assumption that velocity is positive on a given interval guarantees that the movement of an object is always in a single direction, and hence ensures that its change in position is the same as the distance it travels. As we saw in Example4.13, there are natural settings in which an object’s velocity is negative, and we would like to understand this scenario as well.

Consider a simple example where a woman goes for a walk on the beach along a stretch of very straight shoreline that runs east-west. We assume that her initial position is \ = 0\text\) and that her position function increases as she moves east from her starting location. For instance, \ mile represents one mile east of the start location, while \ tells us she is one mile west of where she began walking on the beach.

Now suppose she walks in the following manner. From the outset at \ she walks due east at a constant rate of \ mph for 1.5 hours. After 1.5 hours, she stops abruptly and begins walking due west at a constant rate of \ mph and does so for 0.5 hours. Then, after another abrupt stop and start, she resumes walking at a constant rate of \ mph to the east for one more hour. What is the total distance she traveled on the time interval from \ to \ What the total change in her position over that time?

These questions are possible to answer without calculus because the velocity is constant on each interval. From \ to \ she traveled

On \ to \ the distance traveled is

Finally, in the last hour she walked

## But Wait Which Formula Do I Use

You look at your formula sheet and you have three different ones that are marked under the problems subject. How do you know which one to use?? Naturally, you begin panicking again.

Dont panic.

Physical equations didnt just land on scientists from the sky, all wrapped up nicely in mathematical formulation. They are derived from physical properties, and they are all interconnected. In most physics problems, there is more than one way to reach a solution, often meaning that more than one equation can work. In fact, in the vast majority of questions, no matter what equation you use assuming that it is relevant to the subject matter, and that you insert the proper variables you will reach a solution.

The way to know which equation to use depends on two main issues: the variables given to you in the equation and your experience. The more problems you solve, the more you will become familiar with strategies for picking the right formula. Until that happens, though, look for the formula that has the variable you already know and connects those to the one variable you are missing. If you have two missing variables, you will likely need two equations.

Slow down, look at your variable list, and find the right ones. Its like a puzzle, and the more you do it, the better you get at it.

## Time Velocity And Speed

• Explain the relationships between instantaneous velocity, average velocity, instantaneous speed, average speed, displacement, and time.
• Calculate velocity and speed given initial position, initial time, final position, and final time.
• Derive a graph of velocity vs. time given a graph of position vs. time.
• Interpret a graph of velocity vs. time.

Figure 1. The motion of these racing snails can be described by their speeds and their velocities.

There is more to motion than distance and displacement. Questions such as, How long does a foot race take? and What was the runners speed? cannot be answered without an understanding of other concepts. In this section we add definitions of time, velocity, and speed to expand our description of motion.

## How To Find Velocity From Work

How to Find Speed From Distance & Mass : Math & Physics Lessons

From the above discussion, it is clear that we need a relationship that could relate

• force
• distance and
• velocity

If you are familiar with the concept of work and energy then you must be aware of the following facts

• Kinetic Energy is the energy used for motion. We can say that if an object of mass \ is moving with some velocity \, it has kinetic energy.
• We also know that when a thing moves they do work.

So, when things move they do work, and they have kinetic energy. No work is done if the object does not move, regardless of how much force is applied to it. We also know that when you do work, you produce kinetic energy. The amount of kinetic energy in an object is determined by its mass and velocity. You can calculate velocity from force and distance by equating work and kinetic energy . Since kinetic energy depends on mass, so youll need to know the mass of the moving object to solve your problem.

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## Distance Formula In Physics

If you know how fast and how long something was traveling, you can solve for the distance traveled. You just need to rearrange the velocity formula above to get the distance formula in physics:

A plane travels 150 miles per hour on it’s way from Atlanta to San Diego. How far has the plane traveled in 3.5 hours?

Since the plane appears to be going in one direction in a straight line, you can assume that the change in position equals distance. Plug your known variables into the distance formula:

#### Tips

• Make sure to pay attention to units when using the distance formula in physics. If you’re using a velocity that’s miles per hour, and you’re solving for distance, make sure your time is in hours too.

## Subsectionarea Under The Graph Of The Velocity Function

In Example4.1, we learned that when the velocity of a moving object’s velocity is constant , the area under the velocity curve over an interval of time tells us the distance the object traveled.

The left-hand graph of Figure4.6 shows the velocity of an object moving at 2 miles per hour over the time interval \ The area \ of the shaded region under \\) on \ is

This result is simply the fact that distance equals rate times time, provided the rate is constant. Thus, if \\) is constant on the interval \ the distance traveled on \ is equal to the area \ given by

where \ is the change in \ over the interval. \) on the interval \ we simply chose \\text\) the value at the interval’s left endpoint.) For several examples where the velocity function is piecewise constant, see .1Marc Renault, calculus applets.

The situation is more complicated when the velocity function is not constant. But on relatively small intervals where \\) does not vary much, we can use the area principle to estimate the distance traveled. The right-hand graph of Figure4.6 shows a non-constant velocity function. On the interval \ the velocity varies from \ = 2.5\) down to \ \approx 2.1\text\) One estimate for the distance traveled is the area of the pictured rectangle,

Note that because \ is decreasing on \ \ is an over-estimate of the actual distance traveled.

 \

## Educational Standards Each Teachengineering Lesson Or Activity Is Correlated To One Or More K

###### NGSS: Next Generation Science Standards – Science
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• Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. More Details

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• Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. More Details

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• Technological innovation often results when ideas, knowledge, or skills are shared within a technology, among technologies, or across other fields. More Details

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• Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. More Details

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• Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. More Details

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For the teacher’s introductory presentation and activity preparation:

Each group needs:

• 1 LEGO MINDSTORMS EV3 brick
• 1 ultrasonic sensor
• LEGO MINDSTORMS NXT robot, such as the NXT Base Set

## Time Intervals And Distances #### Differences and values

Wrong Track: Speed is just distancetime, and that’s all there is to it.

Right Lines: Distance is the difference between two locations along your track. To find your speed you also need a time interval, the difference between two times on the clock . So speed is calculated from difference in location along the track and difference in time .

#### Speed is always from someone’s point of view

Where am I now? is a question that requires a position for an answer .

What time is it now? is a question that requires a time for an answer .

Repeat these questions after a journey and you’ll get another position and a different time.

To find a speed you need to combine the two positions, and maybe some more information to find the distance covered on your journey, as well as combine the two clock readings to find the duration of your journey.

Trying to cut corners to make things simpler often stores up difficulties for the future. This is a place to take care. We’d suggest that you avoid using just time, unless you mean time of day. Avoid What’s the time for that journey?, replacing it with something more natural:

Teacher: How long did the journey take?

This kind of phrasing implies a duration, an interval of time. Distance is less of an issue, as we’re less likely to use the word to mean many things, as we do for time .

distance = positionend positionbegin

duration = timeend timebegin

speed = distancetime

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## Determining Tension On A Single Strand

• 1Define the forces on either end of the strand. The tension in a given strand of string or rope is a result of the forces pulling on the rope from either end. As a reminder, force = mass × acceleration. Assuming the rope is stretched tightly, any change in acceleration or mass in objects the rope is supporting will cause a change in tension in the rope. Don’t forget the constant acceleration due to gravity – even if a system is at rest, its components are subject to this force. We can think of a tension in a given rope as T = + , where “g” is the acceleration due to gravity of any objects the rope is supporting and “a” is any other acceleration on any objects the rope is supporting.XResearch source
• For the purposes of most physics problems, we assume ideal strings – in other words, that our rope, cable, etc. is thin, massless, and can’t be stretched or broken.
• As an example, let’s consider a system where a weight hangs from a wooden beam via a single rope . Neither the weight nor the rope are moving – the entire system is at rest. Because of this, we know that, for the weight to be held in equilibrium, the tension force must equal the force of gravity on the weight. In other words, Tension = Force of gravity = m × g.
• Assuming a 10 kg weight, then, the tension force is 10 kg × 9.8 m/s2 = 98 Newtons.
• Ft = Fg + m × a
• Ft = 98 + 10 kg × 1 m/s2
• Ft = 108 Newtons.
• Fc = m × v2/r
• Fc =10 × 2.67 = 26.7 Newtons.
• So, our the total tension would be 98 + 26.7 = 124.7 Newtons.
• T = 980/15
• ## To Find The Image Distance For Varying Object Distances In Case Of A Convex Lens With Ray Diagrams

The lens is a transparent material which is bound by two surfaces. It has a principal axis, principal focus, centre of curvature of lens, aperture and optical centre.There are two types of lenses, they are a convex lens and a concave lens. The images obtained from these lenses can be either a real image or a virtual image. Below is an experiment to find the image distance for varying object distances of a convex lens with ray diagrams.

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