Linear Motion

Quantities

There are several Quantities in Linear Motion

• Distance
• Displacement
• Speed
• Velocity
• Acceleration
• Average value of Velocity and Acceleration
• Instantaneous value of Velocity and Acceleration
• *Vertical Motion*

Equation

There is 3 Equation in Linear Motion

The First one provides the relation between Initial Velocity, Final Velocity, The Time taken to reach it and The Acceleration.

The Second one provides the relation between Distance Traveled, Initial Velocity, Acceleration and Time.

The Third one provides the relation between Initial Velocity, Final Velocity, Acceleration and Distance. There is no time factor in it.

So the Equation is written as:

1st Acceleration = (Final Velocity - Initial Velocity) / Time or Final Velocity = Initial Velocity + Acceleration * Time

2nd Distance/Displacement = Initial Velocity * Time + (Acceleration * Time²) / 2

3rd Final Velocity² = Initial Velocity² + 2 Acceleration * Distance/Displacement

If it is used for a free fall object change all Acceleration to Gravity.

Examples :

1. A ball was released from a building and after 5 seconds it reached the ground. What is the maximum velocity of the ball?

Since it is a free fall the acceleration is 10 m/s² so in equation its 10 = (Final Velocity - 0) / 5

10 * 5 = Final Velocity , so the maximum velocity of the ball is 50 m/s.

2.  A ball was released from a building and after 5 seconds it reached the ground. What is the height of the building?

Since it is a free fall the acceleration is 10 m/s² and the Initial Velocity is 0 m/s so in equation it is

S = 0 * 5 + 10 * 5² / 2

S = 0 + 250 / 2

S = 125 m

So the height of the building is 125 m

3. A plane that starts from rest then with a velocity of 100 m/s and acceleration of 2 m/s² is going to take off. Calculate the minimum distance that must be traveled before taking off.

Since its starting from rest so the Initial Velocity is 0 m/s so in equation it is

100² = 0² + 2 * 2 * S

10000 = 2 * 2 * S

S = 10000 / 4

S = 2500 m

So it needs to travel 2500 m before taking off.

Graph in Linear Motion

In Linear Motion there is two types of graphs, the first one is Position vs Time and the second one is Velocity vs Time.

Position vs Time

There is 2 types of Position vs Time graphs. It is Positive and Negative. If it is Positive it means that it is going forward while if it is Negative it means that it is going backward. 

The Equation is (Final Position - Initial Position) / (Final Time - Initial Time).

To find the result which is velocity, we divide the position with the time. So for this graph its velocity is

(10 - 0) / (5 - 0) = 2 m/s

(20 - 10) / (10 - 5) = 2 m/s

(30 - 20) / (15 - 10) = 2 m/s

So the velocity is 2 m/s going forward while if it is reversed 

(20 - 30) / (5 - 0) = -2 m/s

(10 - 20) / (10 - 5) = -2 m/s

(0 - 10) / (15 - 10) = -2 m/s

So the velocity is -2 m/s going backward it is written in minus but the + and - is just a sign whether it is going forward or backward.

Velocity vs Time

There is 2 types of Velocity vs Time graphs. It is Positive and Negative. If it is Positive it means that it is going forward while if it is Negative it means that it is going backward. 

The equation is (Final Velocity - Initial Velocity) / (Final Time - Initial Time).

To find the result which is acceleration, we divide the velocity with the time. So for this graph its acceleration is

(10 - 0) / (1 - 0) = 10 m/s²

(20 - 10) / (2 - 1) = 10 m/s²

(30 - 20) / (3 - 2) = 10 m/s²

(40 - 30) / (4 - 3) = 10 m/s²

(50 - 40) / (5 - 4) = 10 m/s²

So the acceleration is 10 m/s² going forward while if it is reversed

(40 - 50) / (1 - 0) = -10 m/s²

(30 - 40) / (2 - 1) = -10 m/s²

(20 - 30) / (3 - 2) = -10 m/s²

(10 - 20) / (4 - 3) = -10 m/s²

(0 - 10) / (5 - 4) = -10 m/s²

So the acceleration is -10 m/s² going backward it is written in minus but the + and - is just a sign whether it is going forward or backward.