# 1d kinematic w/ potential energy

• ross_inc
In summary, the homework problem involves finding the equation for a particle moving in one dimension with potential energy U(x) and calculating the time it takes for the particle to move from x0 to 5x0, starting from rest at x0. The given equations for this problem are the equation for kinetic energy (E=mv^2/2-U(x)) and the potential energy function (U(x)=c/x for x>0). The solution involves substituting the given equations into an integral and solving for the time, leaving the answer in terms of m, c, and x0.
ross_inc

## Homework Statement

Equation for a particle moving in one dimension with potential energy U(x):

t=$$\int$$1/$$\sqrt{2(E-U(x))/m}$$ , integrated from x0 to 5x0

Suppose U(x)=c/x for x>0. Calculate the time for the particle to move from x0 to 5x0, starting from rest at x0. Leave the answer in terms of m,c,x0

E=mv2/2-U(x)

U(x)=c/x for x>0

## The Attempt at a Solution

I've been working on this for a few hours, subbing E and U(x) out will give an integral w/ a denominator of:

$$\sqrt{2(mv2/2-2c/x)/m}$$

however that now puts a v into the mix and it specificaly says "solve in terms of m,c, x0". Should i be replacing v with an equation for velovity or somthing? this integral is getting way nasty.

hey, I have this exact same problem, how does one do this?

## 1. What is 1D kinematics with potential energy?

1D kinematics with potential energy is a branch of physics that studies the motion of objects in one dimension while considering the effects of potential energy on the object's motion.

## 2. What is potential energy?

Potential energy is the energy possessed by an object due to its position or state. In 1D kinematics, potential energy is often associated with the object's height above the ground and is measured in joules (J).

## 3. How is potential energy related to kinetic energy?

Potential energy and kinetic energy are two forms of energy that are related to each other. When an object has potential energy, it can be converted into kinetic energy when it is in motion. The equation for this relationship is PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object.

## 4. How is 1D kinematics with potential energy used in real-life situations?

1D kinematics with potential energy is used in a variety of real-life situations, such as calculating the trajectory of a projectile, determining the energy required for an object to reach a certain height, and predicting the motion of a roller coaster or pendulum.

## 5. What are some common misconceptions about 1D kinematics with potential energy?

One common misconception is that potential energy is the same as kinetic energy. In reality, these are two distinct forms of energy with different formulas and units of measurement. Another misconception is that potential energy only applies to objects at rest, when in fact it can also affect the motion of objects in 1D kinematics.

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