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Jared Hill
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Homework Statement
If v(x)=ax-2, then what is its force in terms of x. What is its motion as a function of time when x=a?
It is the motion along a horizontal frictionless plane. I did F=m dv/dt= m dv/dx*dx/dt= -2ma2x-5ehild said:What is v(x)? The motion of what are you speaking about?
Show the relevant equations and your attempt to solve the problem.
How do you specify the motion of a particle at a given time or at a given place? You give the velocity and acceleration. What are they at x=a?Jared Hill said:It is the motion along a horizontal frictionless plane. I did F=m dv/dt= m dv/dx*dx/dt= -2ma2x-5
Then I fould potential energy by integration. However I could not find the motion of the particle.
Sorry for the incomplete question.ehild said:How do you specify the motion of a particle at a given time or at a given place? You give the velocity and acceleration. What are they at x=a?
The relationship between force and motion is described by Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. In other words, the greater the force applied to an object, the greater its acceleration will be, and vice versa.
To calculate the force acting on an object, you can use the equation F = ma, where F is force in Newtons, m is mass in kilograms, and a is acceleration in meters per second squared. Simply plug in the values for mass and acceleration and solve for force.
Weight and force are often used interchangeably, but they are actually two different concepts. Weight is a measurement of the gravitational force acting on an object, while force is a measurement of the push or pull on an object. Weight is dependent on the mass of an object and the strength of the gravitational field, while force is dependent on mass and acceleration.
Force affects an object's motion by changing its velocity. When a force is applied to an object, it will either speed up or slow down, depending on the direction of the force. Additionally, if multiple forces are acting on an object, they can cancel each other out or combine to produce a net force, resulting in different types of motion (e.g. constant velocity, acceleration, etc.).
Yes, you can find the equation of motion for an object with a changing force by using calculus and integrating the equation F = ma. This will give you the equation of motion in terms of position, velocity, and time for an object experiencing a changing force. However, if the force is constant, you can simply use the equations of motion for constant acceleration to find the object's motion.