1. Physics 13 General Physics 1
Kinematics of Motion
Motion along a Straight Line
MARLON FLORES SACEDON

2. TOPICS: Motion along a Straight Line (Rectilinear)
Introduction to Kinematics of Motion
Xt-Graph, vt-graph, at-Graph
Uniformly Accelerated Bodies (UAB)
Free Falling Bodies (FFB)
Motion in Two or Three Dimensions
Velocity vectors and Acceleration vectors
Projectile Motion
Motion in a Circle

3. Motion along a Straight Line: Introduction
What is Kinematics?
A motion of an object without considering outside factors which causes their motion.
Purely descriptive study of motion.
What is motion?
A change in position of particle at certain instance.

4. Motion along a Straight Line: Introduction
How to describe motion?
We can describe motion by…
Position (𝑥)
Time (𝑡)
Displacement (∆𝑥)
Velocity (𝑣)
Acceleration (𝑎)
x𝑡-graph, 𝑣𝑡-graph, & 𝑎𝑡-graph

5. Motion along a Straight Line: Introduction
Describing motion using Time (t) and Position (x)
x 1 , x 2 , x 3 … x n = position of particle from the ref point.
−𝑥 4 − 𝑥 0
𝑥 1 − 𝑥 0
𝑥 𝑛 − 𝑥 0
𝑥 2 − 𝑥 0
𝑥 3 − 𝑥 0
𝑝 4 ( 𝑡 4 , −𝑥 4 )
𝑝 1 ( 𝑡 1 , 𝑥 1 )
𝑝 2 ( 𝑡 2 , 𝑥 2 )
𝑝 3 ( 𝑡 3 , 𝑥 3 )
𝑝 𝑛 ( 𝑡 𝑛 , 𝑥 𝑛 )
𝑟𝑒𝑓
𝑡 4
𝑡 0
𝑡 1
𝑡 2
𝑡 3
𝑡 𝑛
− 𝑥 4
𝑥 0
𝑥 1
𝑥 2
𝑥 3
𝑥 𝑛
𝑥 2 − 𝑥 1
𝑥 3 − 𝑥 2
Displacement ∆𝑥
= change in position
−𝑥 4 − 𝑥 3
𝑥 𝑛 −(− 𝑥 4 )

6. Motion along a Straight Line: 𝑥𝑡-Graph, 𝑣𝑡-Graph, & 𝑎𝑡-Graph
Describing motion using Time (t) and Position (x)
𝑝 4 ( 𝑡 4 , −𝑥 4 )
𝑝 1 ( 𝑡 1 , 𝑥 1 )
𝑝 2 ( 𝑡 2 , 𝑥 2 )
𝑝 3 ( 𝑡 3 , 𝑥 3 )
𝑝 𝑛 ( 𝑡 𝑛 , 𝑥 𝑛 )
𝑟𝑒𝑓
( 𝑡 0 , 𝑥 0 )
Describing motion using 𝑥𝑡-Graph
𝑝 𝑛 ( 𝑡 𝑛 , 𝑥 𝑛 )
𝑡 𝑛
𝑥 𝑛
𝑝 3 ( 𝑡 3 , 𝑥 3 )
𝑡 3
𝑥 3
𝑝 2 ( 𝑡 2 , 𝑥 2 )
Position (𝑥)
𝑡 2
𝑥 2
𝑝 1 ( 𝑡 1 , 𝑥 1 )
𝑥 1
𝑡 1
𝑡 4
- 𝑥 4
Time (𝑡)
𝑝 4 ( 𝑡 4 , 𝑥 4 )

7. Motion along a Straight Line: 𝑥𝑡-Graph, 𝑣𝑡-Graph, & 𝑎𝑡-Graph
Describing motion with velocity
𝑥𝑡-Graph
𝑝 𝑛 ( 𝑡 𝑛 , 𝑥 𝑛 )
𝑡 𝑛
𝑥 𝑛
Velocity of particle from pt.1 to pt.2 or 𝒗 𝟏𝟐 = ∆𝒙 ∆𝒕
𝑣 23 = 𝑥 3 − 𝑥 2 𝑡 3 − 𝑡 2
𝑝 3 ( 𝑡 3 , 𝑥 3 )
𝑡 3
𝑥 3
𝑝 2 ( 𝑡 2 , 𝑥 2 )
Position (𝑥)
( 𝑥 3 − 𝑥 2 )
𝑣 4𝑛 = 𝑥 𝑛 − 𝑥 4 𝑡 𝑛 − 𝑡 4
𝑡 2
𝑥 2
𝑣 12 = 𝑥 2 − 𝑥 1 𝑡 2 − 𝑡 1
( 𝑡 3 − 𝑡 2 )
𝑣 34 = 𝑥 4 − 𝑥 3 𝑡 4 − 𝑡 3
( 𝑥 𝑛 − 𝑥 4 )
( 𝑥 2 − 𝑥 1 )
𝑝 1 ( 𝑡 1 , 𝑥 1 )
(𝑡 2 − 𝑡 1 )
𝑥 1
𝑡 1
( 𝑥 4 − 𝑥 3 )
𝑡 4
- 𝑥 4
(𝑡 𝑛 − 𝑡 4 )
(𝑡 4 − 𝑡 3 )
Time (𝑡)
𝑝 4 ( 𝑡 4 , 𝑥 4 )
The ratio between change in position and time interval is average velocity.
So, the slope between points is average velocity.
The greater the slope, the faster the particle moving. If slope is positive, particle moves towards positive axis, and reverse direction for negative slope. If slope is zero, particle is at rest position.

8. Motion along a Straight Line: 𝑥𝑡-Graph, 𝑣𝑡-Graph, & 𝑎𝑡-Graph
Describing motion with velocity
𝑥𝑡-Graph
𝑝 𝑛 ( 𝑡 𝑛 , 𝑥 𝑛 )
𝑝 3 ( 𝑡 3 , 𝑥 3 )
𝑣 23 = 𝑣 𝐵
𝑣 4𝑛 = 𝑣 𝐷
𝑝 2 ( 𝑡 2 , 𝑥 2 )
Position (𝑥)
𝑡 𝐵 = 𝑡 2 + 𝑡 3 2
𝑣 12 = 𝑣 𝐴
𝑣 34 = 𝑣 𝐶
𝑡 𝐷 = 𝑡 4 + 𝑡 𝑛 2
𝑝 1 ( 𝑡 1 , 𝑥 1 )
𝑡 𝐴 = 𝑡 1 + 𝑡 2 2
𝑡 𝐶 = 𝑡 3 + 𝑡 4 2
Time (𝑡)
𝑝 4 ( 𝑡 4 , 𝑥 4 )

9. Motion along a Straight Line: 𝑥𝑡-Graph, 𝑣𝑡-Graph, & 𝑎𝑡-Graph
Describing motion with acceleration
𝑥𝑡-Graph
𝑣 23 = 𝑣 𝐵
𝑣 4𝑛 = 𝑣 𝐷
Position (𝑥)
𝑡 𝐵
𝑣 12 = 𝑣 𝐴
𝑣 34 = 𝑣 𝐶
𝑡 𝐷
𝑡 𝐴
𝑡 𝐶
Time (𝑡)
Time (𝑡)
Velocity (𝑣)
𝑣𝑡-Graph
𝑣 𝐷
𝑡 𝐷
𝑣 𝐴
𝑡 𝐴
𝑣 𝐵
𝑡 𝐵
𝑣 𝐶
𝑡 𝐶

10. Motion along a Straight Line: 𝑥𝑡-Graph, 𝑣𝑡-Graph, & 𝑎𝑡-Graph
Describing motion with acceleration
Velocity of particle from pt.A to pt.B or 𝒂 𝑨𝑩 = ∆𝒗 ∆𝒕
𝑣𝑡-Graph
Time (𝑡)
Velocity (𝑣)
𝑣 𝐷
𝑡 𝐷
𝒂 𝑨𝑩 = 𝑣 𝐵 − 𝑣 𝐴 𝑡 𝐵 − 𝑡 𝐴 = ∆ 𝑣 𝐴𝐵 ∆𝒕
𝑣 𝐴
𝑡 𝐴
𝑣 𝐵 − 𝑣 𝐴
𝒂 𝑪𝑫 = 𝑣 𝐷 − 𝑣 𝐶 𝑡 𝐷 − 𝑡 𝐶 = ∆ 𝑣 𝐷𝐶 ∆𝒕
𝑣 𝐵
𝑡 𝐵
𝑡 𝐵 − 𝑡 𝐴
𝑣 𝐶
𝑡 𝐶
𝒂 𝑩𝑪 = 𝑣 𝐶 − 𝑣 𝐵 𝑡 𝑐 − 𝑡 𝐴 = ∆ 𝑣 𝐵𝐶 ∆𝒕
The ratio between change in velocity and time interval is average acceleration.
So, the slope between velocities is average acceleration.
The greater the slope, the greater the acceleration of the moving particle. If slope is positive, particle is accelerating, and decelerating for negative slope . If slope is zero, particle moves with constant velocity.

11. Motion along a Straight Line: 𝑥𝑡-Graph, 𝑣𝑡-Graph, & 𝑎𝑡-Graph
Example: The following are points of rectilinear motion in a moving particle: 𝑝 1 (5,10), 𝑝 2 (10,45), 𝑝 3 (15, 90), 𝑝 4 (20,90), 𝑝 5 (25,−10). The units of time interval and positions are in seconds and meters respectively. Calculate the displacements and velocities between points. Then construct the 𝑥𝑡 & vt-Graph of the travel using this graph.
Time 𝑡 𝑖𝑛 𝑠
Position 𝑥 𝑖𝑛 𝑚 10 20 30 40 50 60 70 80 90
−10
𝑝 3
𝑝 4
Time 𝑡 𝑖𝑛 𝑠
Velocity 𝑣 𝑖𝑛 𝑚/𝑠 10 15 5 20 25 10 15 5 20 25
𝑝 𝐵 1
−15
−10 −5 10
−20
𝑝 𝐴
𝑝 𝐶
𝑝 2
xt-Graph
vt-Graph
𝑝 1
𝑝 𝐷
𝑝 5
𝑣 34 = 0 5 =0
𝑡 𝐴 =
=7.5𝑠
𝑡 𝐶 =
=17.5𝑠
𝑣 12 = 35 5 =7𝑚/𝑠
𝑥 12 =45−10=35𝑚
𝑡 12 =10−5=5𝑠
𝑥 23 =90−45=45𝑚
𝑡 23 =15−10=5𝑠
𝑣 23 = 45 5 =9𝑚/𝑠
𝑥 34 =90−90=0
𝑡 34 =20−15=5𝑠
𝑣 45 = −100 5
=−20𝑚/𝑠
𝑡 𝐵 =
=12.5𝑠
𝑡 𝐷 =
=22.5𝑠
𝑥 34 =−10−90=−100𝑚
𝑡 45 =25−20=5𝑠

12. Motion along a Straight Line: 𝑥𝑡-Graph, 𝑣𝑡-Graph, & 𝑎𝑡-Graph
Assignment
Describe your motion within 24 hours using Position & Time, displacements, average velocity, average acceleration, 𝑥𝑡−𝐺𝑟𝑎𝑝ℎ, 𝑣𝑡−𝐺𝑟𝑎𝑝ℎ, & a𝑡−𝐺𝑟𝑎𝑝ℎ.
Your starting point will be here (our Class room) and your time starts NOW….
Note: Solutions should be written in Short sized bond paper. Use graphing paper for the Graphs.

13. To be continued…