Velocity Dependent Force

In summary: You can use the following steps: First find the integral of the function from thepoint to the point, then Integrate the function from the point to the point.In summary, the particle is moving with a constant velocity, but at a certain point a force is applied to slow it down. The force is given by F=ma, where m is the mass of the particle, and c is the speed of light. The acceleration due to the force is given by:acceleration = F/m
  • #36
MichaelTam said:
Are there any way to learn more calculus to get more strategy?
It looks like you need to reread integration basics, paying attention to bounds and to definite and indefinite integrals.
 
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  • #37
I got v(t) = -1/c ln( e^(-c v_0) + bc/m t ).
 
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  • #38
ThEmptyTree said:
I got v(t) = -1/c ln( e^(-c v_0) + bc/m t ).
Good.
 
  • #39
MichaelTam said:
Homework Statement:: MIT pretest.
Relevant Equations:: 𝐅⃗=−𝑏𝑒^(𝑐𝑣)𝐢̂ , find v(t), by using differential equation of F=maHello, would you mind sharing what course this is? I am familiar with edx but can’t find it
 
  • #42
This problem becomes more complex if we alter the initial condition of ##v_0## to be not parallel to x-axis but to have some other direction. For example if ##v_0## is in the y-axis then the differential equation becomes $$m\frac{dv_x}{dt}=-be^{c\sqrt{v_0^2+v_x^2}}$$ and who can solve this
 
<h2>1. What is a velocity dependent force?</h2><p>A velocity dependent force is a type of force that is directly proportional to the velocity of an object. This means that as the velocity of the object increases, the force acting on it also increases.</p><h2>2. How is a velocity dependent force different from a constant force?</h2><p>A constant force remains the same regardless of the velocity of an object, while a velocity dependent force changes in magnitude as the velocity changes. This means that a constant force will have the same effect on an object regardless of its speed, while a velocity dependent force will have a greater effect on a faster moving object.</p><h2>3. What are some examples of velocity dependent forces?</h2><p>Some examples of velocity dependent forces include air resistance, friction, and drag. These forces increase as the velocity of an object increases, making it harder for the object to move at high speeds.</p><h2>4. How is velocity dependent force related to Newton's Second Law of Motion?</h2><p>Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that a velocity dependent force can affect the acceleration of an object, as it is directly related to the net force acting on the object.</p><h2>5. Can a velocity dependent force be negative?</h2><p>Yes, a velocity dependent force can be negative. This means that the force is acting in the opposite direction of the object's velocity. For example, air resistance can be negative when an object is moving in the opposite direction of the force of air resistance, slowing it down.</p>

1. What is a velocity dependent force?

A velocity dependent force is a type of force that is directly proportional to the velocity of an object. This means that as the velocity of the object increases, the force acting on it also increases.

2. How is a velocity dependent force different from a constant force?

A constant force remains the same regardless of the velocity of an object, while a velocity dependent force changes in magnitude as the velocity changes. This means that a constant force will have the same effect on an object regardless of its speed, while a velocity dependent force will have a greater effect on a faster moving object.

3. What are some examples of velocity dependent forces?

Some examples of velocity dependent forces include air resistance, friction, and drag. These forces increase as the velocity of an object increases, making it harder for the object to move at high speeds.

4. How is velocity dependent force related to Newton's Second Law of Motion?

Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that a velocity dependent force can affect the acceleration of an object, as it is directly related to the net force acting on the object.

5. Can a velocity dependent force be negative?

Yes, a velocity dependent force can be negative. This means that the force is acting in the opposite direction of the object's velocity. For example, air resistance can be negative when an object is moving in the opposite direction of the force of air resistance, slowing it down.

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