2. Kinematics of Motion

3. Our GOAL!
To compare and contrast the Aristotelian and Galilean views of motion
To define, compare/contrast distance versus position and displacement
Kinematics of Motion

4. The Physics of Aristotle
versus
The Physics of Galileo
Kinematics of Motion

5. ~Aristotle~
He taught that dynamics (the branch of physics that deals with motion) was primarily determined by the nature of the substance that was moving.
He taught that the substances making up the Earth were different from the substances making up the heavens.
He held that the more perfect substance, the “quintessence”, that made up the heavens had its nature to execute perfect (uniform circular) motion.
Kinematics of Motion

6. Aristotle believes that …
everything on Earth is made up of the four elements, earth, water, air, and fire.
a stone fell to the ground because the stone and the ground were similar in substance (in terms of the basic elements, they were mostly “earth”).
objects only moved as long as they were pushed. Thus, objects on Earth stopped moving once applied forces were removed, and the heavenly spheres only moved because of the action of the Prime Mover, who continually applied the force to the outer spheres that turned the entire heavens.
Kinematics of Motion

7. ~Galileo~
He pioneered the concept of inertia (the resistance of any physical object to any change in its state of motion).
His extensive telescopic observations of the heavens made it more and more plausible that they were not made from a perfect, unchanging substance.
He laid the groundwork (together with the ideas of Kepler and Copernicus) to overthrow the physics of Aristotle, in addition to his astronomy.
Kinematics of Motion

8. Aristotle ~ vs ~ Galileo
Why would an arrow shot from a bow continued to fly through the air after they had left the bow and the string was no longer applying force to them?
Why would a block of wood on a table stopped sliding once the applied force was removed?
Aristotle
Galileo
1. He proposed an answer that the arrow creating a vacuum behind it into which air rushed and applied a force to the back of the arrow.
1. In Galileo’s dynamics, the arrow continued to fly through the air because of its inertia.
2. The wood stopped sliding because the force acting on it was removed.
2. The wood stopped sliding because of another force acting on the wood which is the frictional force.
Kinematics of Motion

9. What is, therefore, a frame of reference?
Motion is relative, meaning, it depends on the frame of reference used.
The answer to the previous question is “NO” if the floor or the ground is your frame of reference but “YES” if you’re using the Sun (or the outer space) as your frame of reference.
What is, therefore, a frame of reference?
Frame of reference – an arbitrary set of axes with reference to which the position or motion of something is described or physical laws are formulated.
Kinematics of Motion

10. +y -y +x -x
origin
Shows the xy-coordinate plane that represents a frame of reference or reference frame.
The origin of the frame of reference is the point of intersection of the x-axis and the y-axis. The location of the origin is arbitrary and not fixed, that means that the origin can be anywhere, depending on where the motion happens and where the observer is.
Note: We will use the symbol x for horizontal motions and use y for vertical motions.
Kinematics of Motion

11. Distance vs Displacement
In defining the terms distance and displacement, we should define first the terms scalar and vector quantities.
Scalar quantity – a quantity which has a magnitude (expressed by a number and a unit of measurement) and no direction.
ex. mass, length, time, etc.
Vector quantity – a quantity which has both magnitude and direction.
ex. velocity, acceleration, force, etc.
Distance is a scalar quantity while displacement is a vector quantity.
Distance is the actual path taken by the object with respect to its origin.
Displacement is the change in position of an object. The magnitude of displacement is the shortest distance between the initial and the final position.
Kinematics of Motion

12. REMEMBER!
Displacement, unlike distance, is a vector quantity that points from an object’s initial position to its final position.
The magnitude of displacement is the shortest distance between the initial and final positions.
The SI-mks unit for distance and displacement is meter (𝑚), but there are common units as well, such as kilometer, mile, centimeter, inch, foot, etc.
Kinematics of Motion

13. Representation of a Displacement
Different representations of a positive displacement:
Ex. ∆𝑥=+100 𝑚
Kinematics of Motion

14. Representation of a Displacement
Different representations of a negative displacement:
Ex. ∆𝑥=−100 𝑚
Kinematics of Motion

15. Sample Problem
A student is on her way to the library and walks 11 meters east of their classroom. Suddenly, a classmate calls her so she turns and moves back 5.8 meters west.
Find her:
a. total distance travelled
b. final displacement
Kinematics of Motion

16. Kinematics: Speed vs Velocity

17. speed, velocity and acceleration.
Speed vs Velocity
In case of motion, we use rates to describe it.
Generally, a rate is a quantity (any quantity)that is divided by time.
𝑟𝑎𝑡𝑒= 𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝑡𝑖𝑚𝑒
In kinematics, we use the following rates:
speed, velocity and acceleration.

18. Speed vs Velocity
When we are looking at a moving object, the most noticeable feature of its motion is its fastness or slowness. This is the object’s speed.
Speed is the rate at which distance is covered, that is, speed is equal to the distance divided by time.
Speed is a scalar quantity whose magnitude tells how fast (or slow) an object is moving, without any regard of its direction.
The SI-mks unit for speed is meter per second (𝑚/𝑠). The other common units are 𝑘𝑚/ℎ and 𝑚𝑖/ℎ.

19. 𝒂𝒗𝒆𝒓𝒂𝒈𝒆 𝒔𝒑𝒆𝒆𝒅= 𝒕𝒐𝒕𝒂𝒍 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒕𝒓𝒂𝒗𝒆𝒍𝒆𝒅 𝒆𝒍𝒂𝒑𝒔𝒆𝒅 𝒕𝒊𝒎𝒆
There are two types of speed, the average speed and instantaneous speed.
Average speed, 𝑣 𝑎𝑣 , is the total distance traveled divided by the elapsed time.
𝒂𝒗𝒆𝒓𝒂𝒈𝒆 𝒔𝒑𝒆𝒆𝒅= 𝒕𝒐𝒕𝒂𝒍 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒕𝒓𝒂𝒗𝒆𝒍𝒆𝒅 𝒆𝒍𝒂𝒑𝒔𝒆𝒅 𝒕𝒊𝒎𝒆
In symbols,
𝒗 𝒂𝒗 = 𝒙 𝒕𝒐𝒕 𝒕

20. 𝒗 𝒂𝒗 = 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑡𝑖𝑚𝑒 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙
To make our description of motion deeper, we use another rate, the average velocity, 𝒗 𝒂𝒗 . Average velocity is the rate of change in position.
Symbolically,
𝒗 𝒂𝒗 = 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑡𝑖𝑚𝑒 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙
𝒗 𝒂𝒗 = ∆ 𝒙 𝑡
𝒗 𝒂𝒗 = 𝒙 𝒇 − 𝒙 𝒊 𝒕
(average velocity)
Average velocity is a vector quantity whose magnitude indicates the speed (fastness or slowness) of a body and a direction that shows where the object is heading. The unit for velocity is the same with the unit for speed, meter per second, 𝑚/𝑠.

21. (instantaneous velocity)
Instantaneous velocity is an object’s speed with direction at a very, very short time interval (approaching zero). Simply said, an object’s instantaneous velocity is just instantaneous speed with a direction.
Instantaneous velocity is symbolized by 𝒗 (the subscript “𝑎𝑣” in the average velocity symbol is dropped).
𝒗 = ∆ 𝒙 ∆𝒕
(instantaneous velocity)
very, very small
Simply say, the instantaneous speed/velocity is the speed/velocity of an object at a particular moment in time.

22. Using the sign convention, +𝒗 means an object is either moving to the right (for a horizontal motion) or going upward (for a vertical motion) with respect to the origin.
On the other hand, −𝒗 indicates an object that is either heading towards left (for a horizontal motion) or downward (for a vertical motion) relative to the origin.

23. Sample Problems
An ambulance rescues a victim m away from the hospital and brings the patient back to the hospital within 0.15 hour. Determine the average speed of the ambulance for the whole trip. Express your answer in mks unit.
An ambulance rescues a victim m away, westward of the hospital. It moves in a straight line and reaches the emergency site 4.3 minutes later and quickly bring the patient to the hospital within the next 3.9 minutes. Determine the average speed and average velocity of the ambulance for the whole trip. Express your answer in mks unit.

24. Sample Problems:
A bicycle travels 12 km in 40 min. What is the average speed of the bicycle in m/s? in km/h?
A car travels 40 km/h for 2.0 h, at 50 km/h for 1.0 h, and at 20 km/h for 0.50 h. What is the average speed of the car (in km/h)?
You run 100 m east in 12 s, then turn around and jog 50 m back toward the starting point in 30 s. Calculate (a) your average speed, and (b) your average velocity for the total trip.
A runner runs 2.5 km in 9 min and then takes 30 min to walk back to the starting point. (a) What is the runner’s average velocity for the first 9 min? (b) What is the average velocity for the time spent walking? (c) What is the average velocity for the whole trip? (d) What is the average speed for the whole trip?