Chapter 2: 2-Dimensional Motion

Chapter 2: 2-Dimensional Motion Chapter 2: 2-Dimensional Motion

Chapter 2: 2-Dimensional Motion 2.1 Position 2.2 Distance and Displacement 2.3 Average Speed and Average Velocity 2.4 Instant Speed and Instant Velocity 2.5 Acceleration 2.6 Linear Motion with acceleration 2.7 Free Fall and the Acceleration of Gravity 2.8 Type of Physic Quantities 2.9 2-Dimensional Motion

Introduction Motion can occur in molecular level to universal level.

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

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 reference point Object coordinate system

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 6 m Object 5 m

2.2 Distance and Displacement The quantities that use to describe the change of object called distance and displacement. A. 1 B. 2 3 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.

2.2 Distance and Displacement 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

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

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

2.2 Distance and Displacement 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)

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

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) B. A. Distance / t Average Velocity The ratio of displacement that object changes its position and time ( t) (Vector quantity) B. A. Displacement / t

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

2.3 Average Speed and Average Velocity 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)

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

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

2.3 Average Speed and Average Velocity 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.

2.3 Average Speed and Average Velocity

2.4 Instant Speed and Instant Velocity 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 slope at that time instantaneous velocity: Velocity at t = 2 s Velocity at t = 0.5 s

2.4 Instant Speed and Instant 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

2.4 Instant Speed and Instant 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 m B.) 1 m/s C.) 1.6 m/s D.) 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 Unit: m/s 2 It is vector quantity.

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/s 2 )

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/s 2, +5.6 m/s 2 ) 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 Use for constant acceleration only These equations called EQUATION OF MOTION

2.6 Linear Motion with acceleration 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.

2.6 Linear Motion with acceleration 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 Create coordinate system, and give + to right direction. (Answer: A.) -0.5 m/s 2 B.) 900 m )

2.6 Linear Motion with acceleration Ex. A car starts from still position at x = 0 with a = 5 m/s 2 for t = 8 s. Then, this car move with constant velocity. Find the position of car at t = 12 s. (Answer: 320 m ) Create coordinate system, and give + to right direction.

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/s 2 Acceleration Direction of free fall directs to the ground

2.7 Free Fall and the Acceleration of Gravity In reality, air resistance causes different acceleration of falling object. In vacuum, every falling has the same acceleration. Question? If we throw a ball to the air, what happens to ball velocity? and what happens to ball acceleration?

2.7 Free Fall and the Acceleration of Gravity Free fall is a linear motion with constant acceleration. Therefore, we can use equation of motion to analyze its parameters Note: g is positive or negative value depending on position, and it always directs to the ground.

2.7 Free Fall and the Acceleration of Gravity To analyze problem of free fall, we can use equation of motion like normal linear motion. 1. Create coordinate system and reference point. 2. Collect information. 3. Select suitable equation. 4. Solve the equation. 5. Recheck the answer.

2.7 Free Fall and the Acceleration of Gravity Ex. John measures the height of Pizza tower using time of falling stone that he release from the top of tower. If falling time is 3 seconds, what is the height of this tower?

2.7 Free Fall and the Acceleration of Gravity 1. Create coordinate system and reference point. We can choose any coordinate systems.

2.7 Free Fall and the Acceleration of Gravity 2. Collect information. 1. Initial velocity (u) = 0 m/s 2. Acceleration is gravity, but we consider upper direction for positive value. Therefore, the gravity is negative value (a = -g = -9.8 m/s 2 ) 3. Time (t) = 3 s 4. Height (h) =? m 3. Select suitable equation.

2.7 Free Fall and the Acceleration of Gravity 4. Solve the equation. 5. Recheck the answer. It is possible. h is negative value. It means that h is lower than referent point.

2.7 Free Fall and the Acceleration of Gravity Try another coordinate system. (answer: h = +44.1 m)

2.7 Free Fall and the Acceleration of Gravity Ex. Throw a stone into the air from point A at the top of building with initial velocity = 20 m/s. The height of this building is 50 m. A stone falls to the ground. Find A.) Time at the top of throwing stone B.) Height of throwing stone from the top of building C.) Time of stone from the top to the building D.) Velocity of stone at the top of building (answer: A.) 2 s, B.) 20 m, C.) 4 s, D.) -20 m/s )

2.9 2-Dimensional Motion 2D motion = 1D motion + 1D motion 1D + 1D = 2D

2.9 2-Dimensional Motion Projectile Motion it is subject to constant acceleration. An object moving through the air near the surface of the earth is subject to the constant gravitational acceleration (g), directed downward

2.9 2-Dimensional Motion

2.9 2-Dimensional Motion Circular Motion The motion of an object in a circle at a constant speed. As an object moves in a circle, it is constantly changing its direction all time.

2.9 2-Dimensional Motion

END OF CHAPTER 2 END OF CHAPTER 2 2-Dimensional Motion