# Force related to distance question

• member 428835
In summary, the problem at hand involves finding the total distance traveled by an object moving up a 15 degree slant, given a force function of time and initial and final velocities. The work/energy equation U=\Delta V_G + \Delta T is useful here, and while impulse may not be needed, it is important to consider forces other than gravity (represented by the \Delta V_G term). Given the force function F(t) and mass, it is possible to integrate a(t) to find v(t) and then again to find d(t), which represents the distance traveled as a function of time. The initial velocity is given, and it is important to consider if the force acts parallel to the plane.
member 428835

## Homework Statement

So I have worked through most of the problem and what I have so far is correct. Basically, I have force as a function of time which, when exerted on an object, moves the object up a 15 degree slant. Given two points in times, my question reduces to finding the total distance traveled within this time period. It should be known I have initial and final velocities.

## Homework Equations

work/energy seems useful here $U=\Delta V_G + \Delta T$

i don't think i need impulse, or namely $\int \sum F dt= \Delta G$ as this deals explicitly with time, which I have already used to get the force function (though I could be wrong)

## The Attempt at a Solution

I was thinking $U=\int F ds = m g sin(15) s + m {{V_2}^2}/2 - m {{V_1}^2}/2$ where $s$ is the distance traveled I am looking for and the force function $F$ is changed to only account for forces other than gravity (since the $\Delta V_G$ term accounts for potential gravity.

but then, since $F$ is a function of time, I'm not sure how to proceed (if you need the force function I can give it, but it's kind of long)

I know both initial and final velocities $V_1 , V_2$

Any ideas would be helpful! Thanks!

Last edited by a moderator:
I would think that given F(t), and the mass, you would integrate a(t) to find v(t) and then again to find d(t) distance a function of time. When you integrate a(t) you have the initial velocity given. Does the force act parallel to the plane?

## 1. What is force related to distance?

Force related to distance refers to the relationship between the amount of force applied to an object and the distance the object moves as a result of that force. This relationship is described by the equation F = m*a, where F is force, m is mass, and a is acceleration.

## 2. How does distance affect force?

The greater the distance an object is moved by a force, the more work is done and therefore the more force is applied. This is because force is equal to the mass of an object multiplied by its acceleration, and the further an object moves, the more acceleration it experiences. So, as distance increases, force also increases.

## 3. What is the relationship between force and distance?

The relationship between force and distance is directly proportional. This means that as distance increases, force also increases, and as distance decreases, force decreases. This relationship is described by the equation F = kx, where k is a constant and x is the distance.

## 4. How does force related to distance affect motion?

The amount of force applied to an object and the distance it is moved affects the object's motion. If a greater force is applied over a longer distance, the object will experience greater acceleration and therefore move faster. Similarly, a lesser force over a shorter distance will result in slower motion.

## 5. What are some real-life examples of force related to distance?

Some common examples of force related to distance include pushing a shopping cart, throwing a ball, and using a lever or pulley. In each of these situations, the amount of force applied and the distance the object is moved are directly related and have an impact on the resulting motion.

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