Linear motion

Linear motion
Linear motion is called one dimensional motion.

A. Quantities of Motions
1) Distance 
2) Displacement
Displacement is defined as the change of position. It's a gap between the initial position ad the final position.
3) Speed
The formula of speed is distance divided by time.
4) Velocity
The formula of velocity is displacement divided by time.
5) Acceleration
The formula of acceleration is velocity divided by time.

• The formula of average acceleration is the change of velocity divided by time

6) Average value of velocity and acceleration
7) Instantaneous of velocity and acceleration

• Instantaneous velocity is the velocity of an object at a certain time.

B. Linear motion with constant velocity
If an object moves with zero acceleration, the velocity of the object remains constant.


C. Vertical motion
Equation of linear motion

• Equation 1

This equation provides the relation between initial velocity, final velocity, the time taken, and acceleration

v = v₀ + a t    

• Equation 2

This equation provides the relation between distance travelled, initial velocity, acceleration, and time

s = v₀ t + 1/2 a t²     

• Equation 3

This equation provides the relation between initial velocity, final velocity, acceleration, and distance

v = (v₀² + 2 a s)^1/2  

Example problem:

1. An airplane accelerates down a runway at 3.20 m/s2 for 32.8 s until is finally lifts off the ground. Determine the    distance traveled before takeoff

a= +3.2 m/s2 t = 32.8 s vi = 0 m/s

Find: d = ??

s = vo*t + 1/2*a*t2

d = (0 m/s)*(32.8 s)+ 0.5*(3.20 m/s2)*(32.8 s)2

d = 1720 m

D. Falling object
Al freely falling object are subjected to uniform acceleration. 
The value of its uniform acceleration is 9.8 m/s-2, which is gravity (denoted by "g"). To apply the linear motion equations to falling object, we have to replace "a" with "g" in those equations. 

v = v₀ + g t  
s = v₀ t + 1/2 g t²    




v = (v₀² + 2 g s)^1/2  

Example problem:

A ball is thrown straight up in the air. If it takes the ball

2 seconds to reach its maximum height, what is the initial velocity?

When in the air, the ball is under the influence of gravity.

On the way up, the speed of the ball will decrease by 10 m / s each second until it reaches a speed of 0 ( maximum height) 

The initial speed must have been 20 m / s.       

You could also use the equation v = v₀ + g × t 

v₀ is the initial velocity.

0 = v₀ + 10 × 2

0 = v₀ + 20

Since 0 = -20 + 20, v₀ = -20

Why do we have a negative?

The equation v = v₀ + g × t is missing something important.

The value g = 10 m / s ² is missing an important math concept.

There should be a negative next to g

v = v₀ + -g × t

0 = v₀ + -10 × 2

0 = v₀ + -20

Since 0 = 20 + -20, v₀ = 20

E. Relation Between Velocity and Slope of Curve x-t

Slope of curve x-t is the representation of velocity in a form of curve x with respect to t.

     This graph indicates that velocity is derived from position and time.

 There are 3 types of slope:

*y = x, x= t

Relationship Between Acceleration and Slope of Curve v-t
The acceleration is represented by the slope of curve v-t.

There are 3 types of slope:

 Negative slope

 Positive slope

 Zero slope

Relationship Between Acceleration and Slope of Curve x-t 
If the curve x-t has an upward curvature, the acceleration is positive
 
  If the curve x-t has an downward curvature, the acceleration is negative