Acceleration

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

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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

 

Tags: Equations for Acceleration