Relation with relativity

Relation to relativity

After completing his theory of special relativity, Albert Einstein realized that forces felt by objects undergoing constant proper acceleration are indistinguishable from those in a gravitational field. This was the basis for his development of general relativity, a relativistic theory of gravity.

This is also the basis for the popular Twin paradox, which asks why one twin ages more rapidly when moving away from his sibling at near light-speed and then returning, since the aging twin can say that it is the other twin that was moving. General relativity solved the "why does only one object feel accelerated?" problem which had plagued philosophers and scientists since Newton's time (and caused Newton to endorse absolute space). In special relativity, only inertial frames of reference (non-accelerated frames) can be used and are equivalent; general relativity considers all frames, even accelerated ones, to be equivalent. (The path from these considerations to the full theory of general relativity is traced in the Introduction to general relativity.)

Formula

The formula for acceleration, when force is constant, is \frac{V_{final}-V_{initial}}{\Delta t}

(Final Velocity - Initial Velocity / Total Time Taken)

it should also be pointed out that:

The expression (Final position - Initial Position) / Total time taken)

is, in fact, velocity.

Putting it all together means:

a = \frac{dv}{dt} = \frac{d^2y}{dt^2}, where a is acceleration, v is velocity, y is position, and t is time.