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Chapter 2: 2-Dimensional Motion
Navapadol Kittiamornkul, Ph. D.
Chapter 2:
2-Dimensional Motion

2.1 Position2.2 Distance and Displacement2.3 Average Speed and Average Velocity2.4 Instant Speed and Instant Velocity2.5 Acceleration2.6 Linear Motion with acceleration2.7 Free Fall and the Acceleration of Gravity2.8 Type of Physic Quantities2.9 2-Dimensional Motion
Chapter 2: 2-Dimensional Motion

Introduction
Motion can occur in molecular level to universal level.

Introduction
Do you see Steven Gerrard?
Over there! He dribbles almost to
the goal. Wow! He is very fast.
Hurry!!!
How are these conversations relate to motion?

Introduction
We can explain about motion using these words.
- Position
- Distance and Displacement
- Speed and Velocity
- Acceleration
In this Chapter, we need to understand these word.

2.1 Position
In motion description, we need to describe position firstly.
We can use reference point and coordinate system to describe the position.
Ref. Point Object
Objectcoordinate system
reference point

2.1 Position
Explain the position of this car in figure A, B and C using Reference point.
A. B. C.

2.1 Position
Explain the position of this tree using coordinate system
Object
6 m
5 m

2.2 Distance and Displacement
The quantities that use to describe the change of objectcalled distance and displacement.
A.
B.
Distance is real motion from starting point to initial point in unit meter.
- The distance from A to B can have many ways depending on its route.
- Distance from initial point to finishing point has many values.- Distance has only magnitude. Therefore it is scalar quantity.
12 3

A.
B.Displacement is a vector that is the shortest distance from the initial to the final position of a point in unit meter.
- The magnitude of displacement can be found by
- Displacement has only one value depending on position

A. B.
A. Plot of distance and time. (it always is positive value)
B. Plot of displacement and time. (it can be negative value)

Find the distance and displacement when this rabbit moves around like a circle.

Ex. A cow starts walking at X = +5 m. It moves to the position of X = -15 m. Finally it comes to the position X = +10 m. Find distance and displacement of this cow.
(Answer: distance = 45 m, displacement = +5 m)

Ex. A boat travel to the south 30 km. Then, move to the west 40 km. Find distance and displacement of this boat.
(Answer: distance = 70 km, displacement = 50 km direct to the south-west)
30 km
40 km

2.3 Average Speed and Average Velocity
Speed and velocity can indicate how fast is object changes its position.
Average Speed The ratio of distance that object changes its position and time (t) (Scalar quantity)
Average Velocity The ratio of displacement that object changes its position and time (t) (Vector quantity)
A.
B.
A.
B.
Distance / t
Displacement / t

A.
B.d
x
Average Speed
Average Velocity
Use S.I. unit: m/s

Ex. A man travels from his home to the north 40 km. in 1 hr. Then, he rests 1 hr., and he travels to the east 30 km. in 1 hr. Find the average speed and average velocity of this man.
(Answer: average speed = 23.3 km/hr., average velocity = 16.67 km/hr direct to the north-east)

We can use graph in order to identify motion of object.
Graph A: Object is still.
Graph B: Object move with constant speed.
A. B.

We can find object velocity using graph of position and time.
A. B.
Ex. Find object velocity using graph A. and B.

When graph of motion looks like this figure, we use displacement in order to calculate its average velocity.
From this graph, we can indicate that this object move with average velocity 1 m/s in range of 4 seconds.

2.4 Instant Speed and Instant Velocity
Velocity at t = 2 s
Velocity at t = 0.5 s
Velocity of red graph always changes. So, we call velocity at any time that instantaneous velocity
We can calculate instantaneous velocity at any time using slopeat that time
instantaneous velocity:

Example of Instantaneous velocity
Which type of speed measured by speed radar?
Average speed / Instantaneous speed
When we tell speed or velocity, we notice that it is instantaneous speed or velocity

Ex. According to the graph of position and time, Find A.) Displacement of first 10 s.B.) Velocity of first 10 s.C.) Average velocity though 25 s. D.) Instantaneous velocity at 15 s.
Answer: A.) 10 mB.) 1 m/sC.) 1.6 m/sD.) 1.5 m/s

2.5 Acceleration
When object changes its velocity, we call that object has acceleration.
If object changes its velocity in t, it is called average acceleration.
Average Acceleration
It is vector quantity.
Unit: m/s2

2.5 Acceleration
Acceleration in 1 Dimension
Constant velocity
Increasing velocity(a and v are in the same direction)
Decreasing velocity(a and v are in opposite direction)

2.5 Acceleration
We can calculate acceleration from slope of graph between velocity and time.
Slope of acceleration at t = 0 s
Slope of average acceleration

2.5 Acceleration
Acceleration between 2 s to 10 s can be calculated by
This calculation called average acceleration.

2.5 Acceleration
Acceleration at any time has to calculate the slope at that time.
Acceleration at any time called Instantaneous acceleration.

2.5 Acceleration
Ex. A car drives to the left with velocity of 30 m/s. Then, it changes velocity to 15 m/s in opposite direction in 2 second. Find average acceleration of this car. (Answer: +22.5 m/s2)

2.5 Acceleration
Ex. Find average acceleration of 1 second of object described in following graph. Moreover, find instantaneous acceleration at t = 0 s
(Answer: +2 m/s2, +5.6 m/s2)
Slope of acceleration at t = 0 s
Slope of average acceleration

2.6 Linear Motion with acceleration
We can analyze linear motion with constant acceleration with following equation
These equations called EQUATION OF MOTION
Use for constant acceleration only

How to solve linear motion using equation of motion.
1. Create coordinate system and reference point.2. Collect information.3. Select suitable equation.4. Solve the equation.5. Recheck the answer.

Ex. A train move decreasingly and constantly 30 m/s to stop using 60 second. Find A.) Acceleration of this train
B.) Displacement of this train
(Answer: A.) -0.5 m/s2
B.) 900 m )
Create coordinate system, and give + to right direction.

Ex. A car starts from still position at x = 0 with a = 5 m/s2 for t = 8 s. Then, this car move with constant velocity. Find the position of car at t = 12 s.
Create coordinate system, and give + to right direction.
(Answer: 320 m )

2.7 Free Fall and the Acceleration of Gravity
Free Fall any motion of an object where gravity is the only force acting upon it, and it has no force acting on it.
Acceleration of free fall is constant value 9.8 m/s2
Acceleration Direction of free fall directs to the ground

2.7 Free Fall and the Acceleration of Gravity
I

chapter 2: 2-dimensional motion - · pdf filechapter 2: 2-dimensional motion. ... we can use...

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