# Acceleration

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

## Acceleration

Acceleration is the rate of change of velocity. Whenever a mass experiences a force, an acceleration is acting.  Acceleration is a vector quantity having magnitude and direction, some of these include displacement, drag, force, lift, momentum, thrust, torque, velocity and weight.

### Acceleration FORMULA

$$a = \frac {\Delta v} {t}$$

$$a = \frac {v_f - v_i} {t}$$

Where:

$$a$$ = acceleration

$$\Delta v$$ = velocity differential

$$v_f$$ = final velocity

$$v_i$$ = initial velocity

$$t$$ = time in which the change occures

Solve for:

$$v = v_i + at$$

$$t = \frac {v - v_i} { a}$$

$$v_i = v - at$$

## Average Acceleration

### Average Acceleration FORMULA

$$\bar {a} = \frac {\Delta v} {\Delta t}$$

Where:

$$\bar {a}$$ = average acceleration

$$\Delta v$$ = velocity differential $$(v_f - v_i)$$

$$\Delta t$$ = time differential $$(t_f - t_i)$$

$$v_f$$ = final velocity

$$v_i$$ = initial velocity

$$t_f$$ = final time

$$t_i$$ = initial time

## Centripetal Acceleration

Centripetal acceleration is acceleration towards the center that keeps an object in an elliptical orbit.

### Centripetal Acceleration Formula

$$a_c = \frac { v^2 } { r }$$

Where:

$$a_c$$ = centripetal acceleration

$$v$$ = velocity

$$r$$ = radius

Solve for:

$$v = \sqrt { a r }$$

$$r = \frac { v^2 } { a }$$

## Constant Acceleration

This is not acceleration at a constant velocity with no change.  Constant acceleration is when a moving body changes its velocity by an equal amount of time.  For an example: 1 second 2 meters, 2 second 4 meters, 3 second 6 meters, 4 second 8 meters, etc. or any such relationship.

### Constant Acceleration Formula

$$a_c = \frac { v_2 \;-\; v_1 } { t_2 \;-\; t_1 }$$

Where:

$$a_c$$ = constant acceleration

$$v_2$$ = velocity of the body at time $$t_2$$

$$v_1$$ = velocity of the body at time $$t_1$$

## Instantaneous Acceleration

Instantaneous acceleration is the acceleration at a particular moment in time along its path.

### Instantaneous Acceleration Formula

$$a_i = \frac { d v_i} {d t }$$

Where:

$$a_i$$ = instantaneous acceleration

$$d$$ = displacement

$$v_i$$ = instantaneous velocity

$$t$$ = time

## Rate of Change in acceleration

The rate of change in acceleration is the change in position or the ratio that shows the relationship of change of an object.

### Rate of Change in acceleration Formula

$$a_c = \frac {d}{t}$$

$$a_c = \frac { a_f \;-\; a_i }{ t }$$

Where:

$$a_c$$ = rate of change in acceleration

$$d$$ = displacement

$$a_f$$ = final acceleration

$$a_i$$ = initial acceleration

$$t$$ = time taken tor change in velocity