# Acceleration

## 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