How to Calculate and Solve for Velocity | Motion

The image above represents velocity. To calculate velocity, three essential parameters are needed and these parameters are angular velocity (ω), amplitude (A) and displacement (y).

The formula for calculating velocity:

v = ω√(A² – y²)

Where;

v = Velocity
ω = Angular Velocity
A = Amplitude
y = Displacement

Let’s solve an example;
Find the velocity when the angular velocity is 7, amplitude is 10 and displacement is 13.

This implies that;

ω = Angular Velocity = 7
A = Amplitude = 10
y = Displacement = 13

v = ω√(A² – y²)
So, v = 7 x √(10² – 13²)
v = 7 x √(100 – 169)
v = 7 x √(-69)

i signifies a complex number = √(-1).

Then, v = 7 x √(69) x √(-1)
v = 7 x √(69)i
That is, v = 7 x 8.30i
v = 7(8.30i)

Therefore, the velocity is 7(8.30i) m/s.

Calculating the Angular Velocity when the Velocity, the Amplitude and the Displacement are Given

ω = ^v / _{√(A² – y²)}

Where;

ω = Angular Velocity
v = Velocity
A = Amplitude
y = Displacement

Let’s solve an example;
Find the angular velocity when the velocity is 28, the amplitude is 14, and the displacement is 10.

This implies that;

v = Velocity = 28
A = Amplitude = 14
y = Displacement = 10

ω = ^v / _{√(A² – y²)}
ω = ²⁸ / _{√(14² – 10²)}
So, ω = ²⁸ / _{√(196 – 100)}
ω = ²⁸ / _√(96)
That is, ω = ²⁸ / _9.79
ω = 2.86

Therefore, the angular velocity is 2.86.

Read more: How to Calculate and Solve for Recoil Velocity | Motion

Calculating the Amplitude when the Velocity, the Angular Velocity and the Displacement are Given

A = √(^v2 / _ω² + y²)

Where;

A = Amplitude
v = Velocity
ω = Angular Velocity
y = Displacement

Let’s solve an example;
Find the amplitude when the velocity is 20, the angular velocity is 8 and the displacement is 4.

This implies that;

v = Velocity = 20
ω = Angular Velocity = 8
y = Displacement = 4

A = √(^v2 / _ω² + y²)
So, A = √(²⁰² / _8² + 4²)
A = √(⁴⁰⁰ / ₆₄ + 16)
A = √(6.25 + 16)
Then, A = √22.25
A = 4.716

Therefore, the amplitude is 4.716.

Calculating the Displacement when the Velocity, the Angular Velocity and the Amplitude are Given

y = √(A² – ^v2 / _ω²)

Where;

y = Displacement
v = Velocity
ω = Angular Velocity
A = Amplitude

Let’s solve an example;
Find the displacement when the velocity is 30, the angular velocity is 25 and the amplitude is 12.

This implies that;

v = Velocity = 30
ω = Angular Velocity = 25
A = Amplitude = 12

y = √(A² – ^v2 / _ω²)
So, y = √(12² – ³⁰² / _25²)
y = √(144 – ⁹⁰⁰ / ₆₂₅)
y = √(144 – 1.44)
Then, y = √142.56
y = 11.939

Therefore, the displacement is 11.939.

How to Calculate and Solve for Velocity Using Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the velocity.

To get the answer and workings of the velocity using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

Web – https://www.nickzom.org/calculator-plus

To get access to the professional version via web, you need to register and subscribe for NGN 1,500 per annum to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator

Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator
Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Motion under Physics.

Now, Click on Velocity under Motion

The screenshot below displays the page or activity to enter your values, to get the answer for the angular velocity according to the respective parameters which are the angular velocity (ω), amplitude (A) and displacement (y).

Now, enter the values appropriately and accordingly for the parameters as required by the  angular velocity (ω) is 10, amplitude (A) is 10 and displacement (y) is 13.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the velocity and presents the formula, workings and steps too.