Most general dependence of acceleration

In summary, the conversation discusses the general form of acceleration and how it can be constant, time-dependent, velocity-dependent, or position-dependent. It is suggested that the acceleration can also depend on other variables, such as higher order derivatives, but the state-space of the system must be considered. The acceleration can be determined from the time history of the velocity or from the mass and force at any given time.
  • #1
fog37
1,568
108
Hello,

Newton's second law, when the mass is constant, tells us that the acceleration ##a=\frac {F}{m}## which produces a simple ODE.

The acceleration is a function that can be constant ##a= constant##, time-dependent ##a(t)##, velocity-dependent ##a(v)##, position dependent ##a(x)##, etc.

What is the most general form of acceleration? Would it be $$a=a(x,t,v)$$ ?

Or can it depend on other variables, like higher order derivatives? I don't think so since those higher derivatives...
 
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  • #2
You should consider the state-space of the system you are considering. A state-space consists of all the information needed to specify the current state of the system. All the variables in the state-space may be needed to define the acceleration as a function.

That being said, if you know the time history of the velocity, then you can determine the acceleration from that as its derivative. Likewise, if you know the mass and force at any time, then the acceleration is ##A = m/F##.
 

FAQ: Most general dependence of acceleration

1. What is the most general dependence of acceleration?

The most general dependence of acceleration is on the net force acting on an object and its mass. This can be expressed mathematically as a = F/m, where a is acceleration, F is net force, and m is mass.

2. How does mass affect acceleration?

According to Newton's Second Law of Motion, the greater the mass of an object, the greater the force needed to accelerate it at a given rate. This means that objects with larger masses will have smaller accelerations compared to objects with smaller masses when the same amount of force is applied.

3. What is the relationship between acceleration and velocity?

Acceleration is the rate of change of velocity. This means that when an object experiences acceleration, its velocity is changing. If the acceleration is positive, the velocity will increase. If the acceleration is negative, the velocity will decrease.

4. How does the direction of the net force affect acceleration?

The direction of the net force acting on an object determines the direction of its acceleration. If the net force is in the same direction as the object's velocity, the object will speed up. If the net force is in the opposite direction of the object's velocity, the object will slow down.

5. Can an object have acceleration without a net force?

No, an object cannot have acceleration without a net force acting on it. This is because acceleration is directly proportional to the net force according to Newton's Second Law. Without a net force, there is no acceleration. However, the object may still have a constant velocity if there is no net force acting on it.

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