How to Calculate and Solve for Period | Motion

The image above represents period.

To compute for period, two essential parameters are needed and these parameters are length (l) and acceleration due to gravity (g).

The formula for calculating period:

T = 2π(√(l / g))

Where;

T = Period
l = Length
g = Acceleration due to gravity

Let’s solve an example;
Find the period when the length is 4 and the acceleration due to gravity is 9.8.

This implies that;

l = Length = 4
g = Acceleration due to gravity = 9.8

T = 2π(√(l / g))
T = 2π(√(4 / 9.8))
T = 2π(√(0.408))
T = 2π(0.6388)
T = 6.28 x 0.6388
T = 4.014

Therefore, the period is 4.014 s.

Calculating the Length when the Period and the Acceleration due to Gravity is Given.

l = (T / 2π)2 x g

Where;

l = Length
T = Period
g = Acceleration due to gravity

Let’s solve an example;
Find the length when the period is 28 and the acceleration due to gravity is 9.8.

This implies that;

T = Period = 28
g = Acceleration due to gravity = 9.8

l = (T / 2π)2 x g
l = (28 / 6.28)2 x 9.8
l = (4.458)2 x 9.8
l = 19.87 x 9.8
l = 194.7

Therefore, the length is 194.7.

Continue reading How to Calculate and Solve for Period | Motion

How to Calculate and Solve for Period | Motion

The image above represents period.

To compute for period, one essential parameter is needed and the parameter is angular velocity (ω).

The formula for calculating period:

T = 2π / ω

Where;

T = Period
ω = Angular Velocity

Let’s solve an example;
Find the period when the angular velocity is 11.

This implies that;

ω = Angular Velocity = 11

T = 2π / ω
T = 6.28 / 11
T = 0.57

Therefore, the period is 0.57 s.

Continue reading How to Calculate and Solve for Period | Motion

How to Calculate and Solve for Angular Velocity | Motion

The image above represents angular velocity.

To Compute for angular velocity, one essential parameter is needed and the parameter is frequency (f).

The formula for calculating angular velocity:

ω = 2πf

Where;

ω = Angular Velocity
f = Frequency

Let’s solve an example;
Find the angular velocity when the frequency is 18.

This implies that;

f = frequency = 18

ω = 2πf
ω = 2 x π x 18
ω = 113.09

Therefore, the angular velocity is 113.09 rad/s.

Continue reading How to Calculate and Solve for Angular Velocity | Motion

How to Calculate and Solve for Acceleration | Motion

The image above represents acceleration.

To compute for acceleration, two essential parameters are needed and these parameters are angular velocity (ω) and radius (r).

The formula for calculating acceleration:

a = ω²r

Where;

a = Acceleration
ω = Angular Velocity
r = Radius

Let’s solve an example;
Given that the angular velocity is 24 and the radius is 12. Find the acceleration?

This implies that;

ω = Angular Velocity = 24
r = Radius = 12

a = ω²r
a = 24² x 12
a = 576 x 12
a = 6912

Therefore, the acceleration is 6912 m/s².

Calculating the Angular Velocity when the Acceleration and the Time is Given.

ω = √a / r

Where;

ω = Angular Velocity
a = Acceleration
r = Radius

Let’s solve an example;
Find the angular velocity when the acceleration is 50 with a radius of 2.

This implies that;

a = Acceleration = 50
r = Radius = 2

ω = √a / r
ω = √50 / 2
ω = √25
ω = 5

Therefore, the angular velocity is 5.

Continue reading How to Calculate and Solve for Acceleration | Motion

How to Calculate and Solve for Acceleration | Motion

The image above represents acceleration.

To compute for acceleration, three essential parameters are needed and these parameters are initial velocity (u), final velocity (v) and time (t).

The formula for calculating acceleration:

a = (v – u) / t

Where;

a = Acceleration
v = Final Velocity
u = Initial Velocity
t = Time

Let’s solve an example;
Find the acceleration when the final velocity is 21, the initial velocity is 10 and time is 8.

This implies that;

v = Final Velocity =21
u = Initial Velocity = 10
t = Time = 8

a = (v – u) / t
a = (21 – 10) / 8
a = 11 / 8
a = 1.375

Therefore, the acceleration is 1.375 m/s².

Calculating the Initial Velocity when the Acceleration, the Final Velocity and the Time is Given.

u = v – at

Where;

u = Initial Velocity
a = Acceleration
v = Final Velocity
t = Time

Let’s solve an example;
Find the initial velocity when the acceleration is 14, the final velocity is 34 and the time is 2.

This implies that;

a = Acceleration = 14
v = Final Velocity = 34
t = Time = 2

u = v – at
u = 34 – (14 x 2)
u = 34 – 28
u = 6

Therefore, the initial velocity is 6 m/s.

Continue reading How to Calculate and Solve for Acceleration | Motion

How to Calculate and Solve for Velocity | Motion

The image above represents velocity.

To compute for velocity, two essential parameters are needed and these parameters are angular velocity (ω) and radius (r).

The formula for calculating velocity:

v = ωr

Where;

v = Velocity
ω = Angular Velocity
r = Radius

Let’s solve an example;
Find the velocity when the angular velocity is 17 with a radius of 6.

This implies that;

ω = Angular Velocity = 17
r = Radius = 6

v = ωr
v = 17 x 6
v = 102

Therefore, the velocity is 102 m/s.

Calculating the Angular Velocity when the Velocity and the Radius is Given.

ω =v / r

Where;

ω = Angular Velocity
v = Velocity
r = Radius

Let’s solve an example;
Given that the velocity is 30 with a radius of 3. Find the angular velocity?

This implies that;

v = Velocity = 30
r = Radius = 3

ω = v / r
ω = 30 / 3
ω = 10

Therefore, the angular velocity is 10.

Continue reading How to Calculate and Solve for Velocity | Motion

How to Calculate and Solve for Distance Covered | Motion

The image above represents distance covered.

To compute for distance covered, three essential parameters are needed and these parameters are initial velocity (u), acceleration (a) and time (t).

The formula for calculating distance covered:

S = ut + 0.5at²

Where;

S = Distance Covered
u = Initial Velocity
t = Time
a = Acceleration

Let’s solve an example;
Find the distance covered when the initial velocity is 21, acceleration is 10 and the time is 15.

This implies that;

u = Initial Velocity = 21
t = Time = 15
a = Acceleration = 10

S = ut + 0.5at²
S = (21 x 15) + (0.5 x 10 x 15²)
S = 315 + (0.5 x 10 x 225)
S = 315 + (1125)
S = 1440

Therefore, the distance covered is 1440 m .

Calculating the Initial Velocity when the Distance Covered, the Acceleration and the Time is Given.

u = S – 0.5at2 / t

Where;

u = Initial Velocity
S = Distance Covered
t = Time
a = Acceleration

Let’s solve an example;
Find the initial velocity when the distance covered is 48 with a time of 8 and an acceleration of 9.

This implies that;

S = Distance Covered = 48
t = Time = 8
a = Acceleration = 9

u = S – 0.5at2 / t
u = 48 – 0.5(9)(82) / 8
u = 48 – 0.5(9)(64) / 8
u = 48 – 288 / 8
u = – 240 / 8
u = – 30

Therefore, the initial velocity is – 30 m/s.

Continue reading How to Calculate and Solve for Distance Covered | Motion

How to Calculate and Solve for Final Velocity | Motion

The image above represents final velocity.

To compute for final velocity, three essential parameters are needed and these parameters are initial velocity (u), acceleration (a) and distance covered (S).

The formula for calculating final velocity:

v = √(u² + 2as)

Where;

v = Final Velocity
u = Initial Velocity
a = Acceleration
s = Distance Covered

Let’s solve an example;
Find the final velocity when the initial velocity is 13, acceleration is 9.8 and the distance covered is 32.

This implies that;

u = Initial Velocity = 13
a = Acceleration = 9.8
s = Distance Covered = 32

v = √(u² + 2as)
v = √(13² + (2 x 9.8 x 32))
v = √(169 + (627.2))
v = √(796.2)
v = 28.21

Therefore, the final velocity is 28.21 m/s.

Calculating the Initial Velocity when the Final Velocity, the Acceleration and the Distance Covered is Given.

u = √v² – 2as

Where;

u = Initial Velocity
v = Final Velocity
a = Acceleration
s = Distance Covered

Let’s solve an example;
Find the initial velocity when the final velocity is 30, the acceleration is 8 and the distance covered is 11.

This implies that;

v = Final Velocity = 30
a = Acceleration = 8
s = Distance Covered = 11

u = √v² – 2as
u = √30² – 2(8 x 11)
u = √900 – 2(88)
u = √900 – 176
u = √724
u = 26.90

Therefore, the initial velocity is 26.90 m/s.

Continue reading How to Calculate and Solve for Final Velocity | Motion

How to Calculate and Solve for Distance Covered | Motion

The image above represents distance covered.

To compute for distance covered, two essential parameters are needed and these parameters are angular displacement (θ) and radius (r).

The formula for calculating distance covered:

S = rθ

Where;

S = Distance Covered
r = Radius
θ = Angular Displacement

Lets’s solve an example;
Find the distance covered when the angular displacement is 22 and the radius is 14.

This implies that;

r = Radius = 14
θ = Angular Displacement = 22

S = rθ
S = 6 x 16
S = 96

Therefore, the distance covered is 96 m.

Calculating the Radius when the Distance Covered and the Angular Displacement is Given.

r = S / θ

Where;

r = Radius
S = Distance Covered
θ = Angular Displacement

Lets’s solve an example;
Find the radius when the distance covered is 70 and the angular displacement is 30.

This implies that;

S = Distance Covered = 70
θ = Angular Displacement = 30

r = S / θ
r = 70 / 30
r = 2.3

Therefore, the radius is 2.3.

Continue reading How to Calculate and Solve for Distance Covered | Motion

How to Calculate and Solve for Distance Covered | Motion

The image above represents distance covered.

To compute for distance covered, three essential parameters are needed and these parameters are final velocity (v), initial velocity (u) and time (t).

The formula for calculating distance covered:

S = ((u + v) / 2) t

Where;

S = Distance Covered
u = Initial Velocity
v = Final Velocity
t = Time

Let’s solve an example;
Find the distance covered when the initial velocity is 6, final velocity is 11 and time is 14.

This implies that;

u = Initial Velocity = 6
v = Final Velocity = 11
t = Time = 14

S = ((u + v) / 2) t
S = ((6 + 11) / 2) 14
S = ((17) / 2) 14
S = (8.5) 14
S = 119

Therefore, the distance covered is 119 m.

Calculating the Initial Velocity when the Distance Covered, the Final Velocity and the Time is Given.

u = (2S / t) – v

Where;

u = Initial Velocity
S = Distance Covered
v = Final Velocity
t = Time

Let’s solve an example;
Find the initial velocity when the distance covered is 48, the final velocity is 20 and the time is 4.

This implies that;

S = Distance Covered = 48
v = Final Velocity = 20
t = Time = 4

u = (2S / t) – v
u = (2(48) / 4) – 20
u = (96 / 4) – 20
u = 24 – 20
u = 4

Therefore, the initial velocity is 4 m/s.

Continue reading How to Calculate and Solve for Distance Covered | Motion