# Velocity

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Velocity ( $$v$$ ) (VEL) is the rate of change or displacement with time.  Velocity is a vector quantity having magnitude and direction. The scalar absolute value of magnitude of the velocity vector is the speed of the motion.

Speed ( $$u$$ ) is the rate of change or distance with time.  Speed is a scalar quantity having direction.

Speed is a scalar quantity having direction, some of these include area, density, energy, entropy, length, mass, power, pressure, temperature, volume, and work

Velocity is a vector quantity having magnitude and direction, some of these include acceleration, displacement, drag, force, lift, momentum, thrust, torque, and weight.

### Velocity Formula

$$\large{ v = \frac { d } { t } }$$

$$\large{ s = \frac { d } { t } }$$

$$\large{ v = v_i + at }$$

$$\large{ v_i = v - at }$$

Where:

$$\large{ v }$$ = velocity

$$\large{ a }$$ = acceleration

$$\large{ d }$$ = displacement velocity

$$\large{ d }$$ = distance speed

$$\large{ s }$$ = speed

$$\large{ t }$$ = time

$$\large{ v_i }$$ = initial velocity

Solve for:

$$\large{ t = \frac { d } { v } }$$

$$\large{ t = \frac { d } { s } }$$

## Angular Velocity

Angular velocity ( $$\theta$$ ) (angular speed) is how quickly an object moves through an angle.

### Angular Velocity Formula

$$\large{ \omega = \frac { \theta } { t } }$$

$$\large{ \omega = \frac { \Delta A } { t } }$$

Where:

$$\large{ \omega }$$   (Greek symbol omega) = angular velocity

$$\large{ \Delta A }$$ = change in angle displacement

$$\large{ t }$$ = time

$$\large{ \theta }$$   (Greek symbol theta) = angle distance

## Average Velocity change in Velocity

When an object make changes in its velocity at different times that is an average velocity of any given velocities.

### Average Velocity change in Velocity FORMULA

$$\large{ \bar {v}= \frac { v_1 \;+\; v_2 \;+\; v_3 ... v_n } { t_1 \;+\; t_2 \;+\; t_3 ... t_n } }$$

$$\large{ \bar {v}= \frac { v_1 \;+\; v_2 \;+\; v_3 ... v_n } { n } }$$

Where:

$$\large{ \bar {v} }$$ = average of velocity

$$\large{ n }$$ = total time

$$\large{ t }$$ = time

$$\large{ v }$$ = velocity

## Average Angular Velocity change in Velocity

When an object makes changes in its angular velocity at different times that is an average angular velocity of any given velocities.

### Average Angular Velocity change in Velocity FORMULA

$$\large{ \bar {\omega} \;= \; \frac { \omega_1 \;+\; \omega_2 \;+\; \omega_3 ... \omega_n } { t_1 \;+\; t_2 \;+\; t_3 ... t_n } }$$

$$\large{ \bar {\omega} = \frac { \omega_t } { t_t } }$$

Where:

$$\large{ \bar {\omega} }$$   (Greek symbol omega) = average angular velocities

$$\large{ t }$$ = time

$$\large{ t_t }$$ = total time

$$\large{ \omega }$$   (Greek symbol omega) = angular velocity

$$\large{ \omega_t }$$   (Greek symbol omega) = total angular velocity

## Final Velocity

### Final Velocity FORMULA

$$\large{ v_f = v_i \;+\; at }$$

$$\large{ v_f = 2 \bar {v} \;-\; v_i }$$

Where:

$$\large{ v_f }$$ = final velocity

$$\large{ a }$$ = acceleration

$$\large{ t }$$ = time

$$\large{ \bar {v} }$$ = average velocity

$$\large{ v_i }$$ = initial velocity

## Fluid Velocity

Fluid velocity is how fast the process is traveling in a pipe.  To calculate the velocity of the fluid, use one of the equations below.

To get flow rate in Feet per Second

• Step 1 - Convert the flow rate to cubic feet per second.  This is done by multiplying the flow rate by one of the values shown on the Cubic Feet per Second page.
• Step 2 - divide by the flow area.  The information for flow area can be found on the Carbon Steel Pipe Properties page.  Make sure that the units match and convert the area into square feet.

### Fluid Velocity FORMULA

$$\large{ v = \frac { Q } { A } }$$

Where:

$$\large{ v }$$ = velocity

$$\large{ A }$$ = area

$$\large{ Q }$$ = volumetric flow rate

## Impulse Velocity

Impulse is a change in momentum of an mass when a force is applied.

### Impulse Velocity formula

$$\large{ I = m \Delta v }$$

Where:

$$\large{ I }$$ = impulse velocity

$$\large{ m }$$ = mass

$$\large{ \Delta v }$$ = velocity differential

Solve for:

$$\large{ m = \frac {I} {\Delta v} }$$

$$\large{ \Delta v = \frac {I} {m} }$$

## Instantaneous Velocity

Instantaneous velocity is the derivative (a variable as it approaches 0) of distance with respect to time.