# 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 (Ï‰), amplitude (A)Â andÂ displacement (y).

The formula for calculating velocity:

v = Ï‰âˆš(AÂ² – yÂ²)

Where;

v = Velocity
Ï‰ = 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;

Ï‰ = Angular Velocity = 7
A = Amplitude = 10
y = Displacement = 13

v = Ï‰âˆš(AÂ² – yÂ²)
So, v = 7 x âˆš(10Â² – 13Â²)
v = 7 x âˆš(100 – 169)
v = 7 x âˆš(-69)

i signifies a complex number = âˆš(-1).

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

Therefore, theÂ velocityÂ isÂ 7(8.30i) m/s.

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

Ï‰ = v / âˆš(A2 – y2)

Where;

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Ï‰ = 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

Ï‰ = v / âˆš(A2 – y2)
Ï‰ = 28 / âˆš(142 – 102)
So, Ï‰ = 28 / âˆš(196 – 100)
Ï‰ = 28 / âˆš(96)
That is, Ï‰ = 28 / 9.79
Ï‰ = 2.86

Therefore, theÂ angular velocityÂ isÂ 2.86.

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

A = âˆš(v2 / Ï‰2 + y2)

Where;

A = Amplitude
v = Velocity
Ï‰ = 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
Ï‰ = Angular Velocity = 8
y = Displacement = 4

A = âˆš(v2 / Ï‰2 + y2)
So, A = âˆš(202 / 82 + 42)
A = âˆš(400 / 64 + 16)
A = âˆš(6.25 + 16)
Then, A = âˆš22.25
A = 4.716

Therefore, theÂ amplitudeÂ isÂ 4.716.

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

y = âˆš(A2v2 / Ï‰2)

Where;

y = Displacement
v = Velocity
Ï‰ = 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
Ï‰ = Angular Velocity = 25
A = Amplitude = 12

y = âˆš(A2v2 / Ï‰2)
So, y = âˆš(122302 / 252)
y = âˆš(144 – 900 / 625)
y = âˆš(144 – 1.44)
Then, y = âˆš142.56
y = 11.939

Therefore, theÂ displacementÂ isÂ 11.939.

### How to Calculate and Solve for Velocity Using Nickzom Calculator

Nickzom Calculator â€“Â The Calculator Encyclopedia is capable of calculating the velocity.

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

You can get this app via any of these means:

To get access to theÂ professionalÂ version via web, you need toÂ registerÂ andÂ subscribeÂ forÂ NGN 1,500Â perÂ annumÂ to have utter access to all functionalities.
You can also try theÂ demoÂ version viaÂ https://www.nickzom.org/calculator