About acceleration and time

In summary, classical physics concepts treat time differently in terms of velocity and acceleration. While acceleration remains unchanged under time reversal, velocity is reversed. This means that the laws of physics are the same under time reversal, but the initial conditions may change. It is important to note that reversing time does not necessarily mean time is negative.
  • #1
Hello there, i have a question that confuses me a lot. Is there a difference between the way that we think about time in many classical physics concepts as if it goes to a negative number. For example, we have dv/dt and we can be sure if velocity increases with respect to time and respect to our inertial frame that the acceleration is non zero (positive or negative). If i plug -dt and i don't know if there is a such thing, velocity becomes negative and i can image the motion like a trajectory starts to reverse its motion. But in the dx^2/d^2t the acc doesn't change its sign. What does it mean? Could we think that if time goes to positive or negative, shouldn't it be the same ? Thank you
 
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  • #2
universal2013 said:
But in the dx^2/d^2t the acc doesn't change its sign. What does it mean? Could we think that if time goes to positive or negative, shouldn't it be the same ?
This is the correct one. Acceleration is second order in time: ##a=\frac{d^2}{dt^2}x##. So acceleration is unchanged under time reversal. And therefore force is also unchanged.

In contrast velocity is first order in time: ##v=\frac{d}{dt}x##. So velocity is reversed under time reversal.

That means that the laws of physics* (which describe the forces) are the same under time reversal, and what changes are some of the initial conditions.

*Excluding thermodynamics
 
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Imagine a particle moving towards the right and slowing down. Suppose you have a strobe light flashing at regular intervals of time. Each time the strobe light flashes it reveals the location of the particle. The dots in the following drawing show those locations:

upload_2018-10-15_11-16-15.png


Let's say the velocity is positive, which would make the acceleration negative. If you reverse time you see that the particle would move to the left, speeding up. Now the velocity is negative but the acceleration is also negative! Note that in both cases the acceleration is directed to the left, and so is the net force.

As @Dale says, the acceleration and the force are unchanged under time reversal.

Also, note that when you make ##dt## negative you are not necessarily making ##t## negative. That is, having time go backwards is not the same thing as time being negative.
 

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Thanks for the answers!
 

1. What is acceleration?

Acceleration is the rate at which an object's velocity changes over time. It is measured in meters per second squared (m/s²). This means that for every second an object is accelerating, its velocity increases by that many meters per second.

2. How is acceleration calculated?

Acceleration can be calculated by dividing the change in velocity by the change in time. The formula for acceleration is a = (vf - vi)/t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

3. What is the difference between average and instantaneous acceleration?

Average acceleration is the overall rate of change in an object's velocity over a period of time, while instantaneous acceleration is the rate of change in an object's velocity at a specific moment in time. Average acceleration is calculated by dividing the total change in velocity by the total change in time, while instantaneous acceleration is calculated by taking the derivative of an object's velocity with respect to time.

4. What is the relationship between acceleration and time?

The relationship between acceleration and time is directly proportional. This means that as the time increases, the acceleration also increases, and vice versa. This can be seen in the formula for acceleration, where time is in the denominator. Therefore, the longer an object accelerates, the greater its change in velocity will be.

5. Can time affect an object's acceleration?

Yes, time can affect an object's acceleration. The longer an object accelerates, the greater its change in velocity will be. Additionally, the acceleration of an object can change over time. For example, an object may start with a low acceleration and gradually increase to a higher acceleration, depending on the forces acting on it.

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