# Acceleration and time question

• ErnieDouglas
In summary, the distance between two objects would not appear to increase for an observer on one object if they are moving at a constant velocity on parallel lines, but it would depend on the relationship between their accelerations if they are not moving at a constant velocity.
ErnieDouglas
if two objects were accelerating on parallel lines, would it appear to an observer on one object that the distance apart was increasing, due to special relativity?

Welcome to PF!

Hi ErnieDouglas! Welcome to PF!
ErnieDouglas said:
if two objects were accelerating on parallel lines, would it appear to an observer on one object that the distance apart was increasing, due to special relativity?

If they're "level" with each other, definitely no

"sideways" length is never altered.

If they're not level, it depends how the accelerations are related …

does a stationary observer regard one as always a constant distance ahead of the other (in which case, yes), or are they "rigidly" connected, like the front and back of a train (in which case, no)?

Based on the principles of special relativity, it is possible that an observer on one accelerating object would perceive the distance between the two objects to be increasing. This is because the concept of simultaneity is relative and can vary depending on the relative motion of the two objects. As the objects accelerate on parallel lines, their relative motion would cause a difference in the perception of time and distance between the two objects. Therefore, it is possible for an observer on one object to perceive the distance between them to be increasing due to the effects of special relativity.

## What is acceleration?

Acceleration is the rate at which an object changes its velocity over time. It is measured in units of distance per time squared, such as meters per second squared (m/s^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.

## What is the difference between average and instantaneous acceleration?

Average acceleration is the change in velocity over a specific period of time, while instantaneous acceleration is the acceleration at a specific moment in time. Average acceleration can be calculated using the formula a = (vf - vi) / t, while instantaneous acceleration can be calculated using the derivative of an object's position with respect to time.

## How does acceleration affect an object's motion?

Acceleration can affect an object's motion by changing its velocity. If an object has a positive acceleration, it will speed up; if it has a negative acceleration, it will slow down. The direction of the acceleration will also determine the direction of the change in velocity.

## What is the relationship between acceleration and time?

The relationship between acceleration and time is that acceleration is directly proportional to time. This means that as time increases, so does the acceleration, assuming the other variables (such as velocity) remain constant. This can be seen in the formula a = (vf - vi) / t, where the longer the time interval, the greater the acceleration.

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