Kinematics in One Dimension : Kinematics in One Dimension
PowerPoint Presentation : Branches of Physics : Main Branches : Electrodynamics, Astrophysics, mechanics, thermodynamics, quantum mechanics, nuclear physics etc. Mechanics : Focuses on the motion of an object and forces that causes motion. Mechanics Statics Dynamics Kinematics Kinetics
PowerPoint Presentation : Statics : It deals with bodies at rest under the action of forces. Dynamics : It deals with the bodies under the motion acted upon by force. It is further classified into kinematics and kinetics. Kinetics : It deals with motion of bodies considering cause of motion . Kinematics : It deals with motion of bodies without considering cause of motion. It doesn’t consider the forces causing the motion .
PowerPoint Presentation : Dimension : The number coordinates required to specify the position of an object. length, width and height are three basic dimensions. A body in motion changes its position and so the number of coordinate vary. Classification of motion : One dimensional motion Two dimensional motion Three dimensional motion
PowerPoint Presentation : Kinematics In One dimension : Studies motion of the body along a straight line. Motion in one dimension : For the body moving from A to B, coordinates changes from x1 to x2.
PowerPoint Presentation : Examples of one dimensional motion are: 1. Motion of a train along a straight line 2. An object, like a ball, falling freely, vertically under gravity
PowerPoint Presentation : Bodies at ‘Rest’: A body is said to be at rest if its position doesn’t change with respect its surroundings. e.g. a clock hanging on the wall, a suitcase in a car, a book kept on the table etc. Body in ‘Motion’ : A body is said to be in motion if its position changes with respect its surroundings. e.g. A moving car, a lift moving upward/ downward.
PowerPoint Presentation : “Motion is Relative” e.g. 1. consider two persons in a lift which is moving upwards, the persons are not in motion with respect to each other but for a person outside the lift, two persons are in motion. 2. A person sitting in the car/train.
PowerPoint Presentation : Scalars and Vectors : All physical quantities are classified as scalars or vectors. Scalars : The physical quantities which can be specified by only magnitude (numerical value and unit) are scalar quantities. e.g. mass, time, temperature etc. Vectors : The physical quantities need both magnitude and direction to be defined. e.g. force, velocity, displacement, acceleration.
PowerPoint Presentation : Examples of scalar and vector quantity : Scalar – distance Vector - displacement A person walks A - B => East 3km B – C => North 4km
PowerPoint Presentation : Measure distance : Measuring actual length of the path travelled . Direction is not important. distance => AB + BC = 3km + 4km = 7km Measuring displacement : Measuring shortest path between initial and final position . Displacement => AC. AC = √AB² + √AC² = 5km The displacement is in the direction from A to C. Displacement needs both magnitude and direction and hence it is a vector quantity.
PowerPoint Presentation : Geometrical representation of a vector : A vector is represented by a line segment with an arrow head. A B Length of the line segment (AB) is proportional to the magnitude of the vector. The arrow head indicates the direction of the vector.
PowerPoint Presentation : Example : Consider a man walking along a straight path from P to Q, the length of the path is 100m, then the displacement is represented by P Q Direction : Arrow head Magnitude : length of the line drawn to scale , 1cm = 20m
PowerPoint Presentation : Distance : Length of the path travelled by the body. SI unit : meter Displacement : The shortest distance between initial and final position of the body. It is a vector quantity. magnitude : magnitude of straight line path between initial and final position. Direction : along the straight line drawn from initial to final position.
PowerPoint Presentation : Notes : 1.Distance covered by a body is always greater or equal to magnitude of the displacement. 2. Distance and magnitude of displacement of a body will be equal if and only if the body travel along the shortest path without change in direction. 3. AB ≠ BA as initial and final positions are different.
PowerPoint Presentation : Example : A horse is tied to a rope of length 5m and the other end of the rope is tied to a pole. Find the displacement and distance travelled by the horse in following cases. When the horse makes half revolution along the circular path. When it makes one full revolution When it makes ¾ of the revolution
PowerPoint Presentation : Speed : The rate at which a particle covers a distance along a given path. SI unit is m/s. Scalar quantity Instantaneous speed : The speed of the body at given instant. e.g. Speedometer in vehicle speed = distance traveled (s) / time (t)
PowerPoint Presentation : Uniform speed : Body travels equal distance in equal interval of time. Variable speed : The instantaneous speed changes with time.
PowerPoint Presentation : Average speed : Average speed = total distance total time Velocity : Rate of displacement . velocity = displacement time Velocity is vector quantity SI unit is m/s
PowerPoint Presentation : Examples: 1.Consider a person moving 3km east of A. He then turns north and moves 4km in total time 2 hours. Find the velocity and speed.
PowerPoint Presentation : 2. What is the displacement of the cross-country team if they begin at the school, run 10 miles and finish back at the school? a. 10 miles b. 20 miles c. 5 miles d. 0 miles
PowerPoint Presentation : 3. In the qualifying round of the 50-yd freestyle in the sectional swimming championship, Dugan got an early lead by finishing the first 25.00 yd in 10.01 seconds. Dugan finished the return leg (25.00 yd distance) in 10.22 seconds. a. Determine Dugan's average speed for the entire race. b. Determine Dugan's average speed for the first 25.00 yd leg of the race. c. Determine Dugan's average velocity for the entire race.
PowerPoint Presentation : 4. A cyclist completes 100km race in 2: 25: 30 (hr: min: sec). The race course precedes 50km north, then 25km east, the 25km south. Her split times were 1: 06: 05 at the 50km point and 1: 49: 19 at the 75km point. a. What were her average speeds over the three intervals (50km, 50-75km, 75-100km) how do these speeds compare to her average speed over the whole race? b. What is the displacement from the start to finish? c. What is her average velocity from start to finish? (Both in magnitude and direction)
PowerPoint Presentation : 5. A person taps his finger repeatedly. Their finger travels 2.5 cm before making contact with the tabletop. The finger tapping noise is heard once every 0.20 seconds. What is the speed of the finger with the table?
PowerPoint Presentation : Uniform Velocity : Equal displacements in equal interval of time . Example : B 1S 1S 1M A 1M AB = 10m. Body covers 1m in every 1s -> Uniform velocity Speed and magnitude of velocity is the same along the linear path.
PowerPoint Presentation : Non Uniform Velocity : Consider the motion of particle along the curve. speed of the particle remains constant but the velocity changes since the direction of the velocity changes. (magnitude of velocity remains same )
PowerPoint Presentation : Instantaneous Velocity : The velocity of a particle at a given instant. e.g. Speedometer in car shows instantaneous velocity. Average Velocity : The ratio of total displacement to total time taken. Average Velocity = Total Displacement Total Time
PowerPoint Presentation : Acceleration : Rate of change of Velocity. A body moving with variable velocity is said to posses acceleration. Acceleration = Change in Velocity time Acceleration a = v – u t u = initial velocity v = final velocity t = time
PowerPoint Presentation : Notes : Acceleration is vector as velocity is vector. SI unit m/s2 Positive acceleration : The velocity increases with respect to time. (v > u) Deceleration or retardation : velocity decreases with respect to time. Uniform acceleration : Equal changes in velocity in equal interval of time. If body is moving with uniform acceleration, then its average velocity is given by V(average) = v + u 2
PowerPoint Presentation : Examples : 1. Arlene lands from jump and reduces the downward speed of her centre of mass from 6m/s to 4m/s during the first 0.05 s after impact. If the upward direction is positive, what is the average acceleration of her CM?
PowerPoint Presentation : 2. A baseball is thrown horizontally at 45 m/s. The ball slows down at a rate of 5 m/s2. How long is the ball in the air before coming to rest
PowerPoint Presentation : Equations of Motion : Three important equations of motion. V = u +at S = ut + 1/2at² v² = u² + 2as Where u = initial velocity v = final velocity a = uniform acceleration s = displacement
PowerPoint Presentation : A car is traveling at 30 m/s when the brakes are applied with a constant deceleration of 2 m/s2. What is the change in velocity after 5 seconds? a. 23m/s b. 20m/s c. 56m/s d. 17m/s
PowerPoint Presentation : Calculate the final velocity of a vehicle accelerating at 2.0 m/s/s after 3.0 s if the vehicle starts from rest. a. 17 m/s b. 9.07 m/s c. 12.7 m/s d. 6 m/s
PowerPoint Presentation : A dragster accelerates to a speed of 112 m/s over a distance of 398 m. Determine the acceleration (assume uniform) of the dragster
PowerPoint Presentation : A worker drops a hammer from the top of a 60m high building. If the speed of sound in air is 340 m/s, how long does the worker have to shout down to warn colleagues (if his warning is to reach them before the hammer!) Neglect air resistance.
PowerPoint Presentation : Ans : The solution is, the length of time for the hammer to reach the ground minus the length of time it takes for the shouted warning to reach the workers on the ground. For the hammer: Initial speed u = 0 Acceleration a = 9.81 m/s2 Distance s = 60m Use s = ut + ½ at² find t ? t = 3.5s For the shout s / t = 340 t = 0.18s Difference in travel time between hammer and shout: 3.5 - 0.18 = 3.32 s The warning must be shouted within 3.32 seconds of dropping the hammer. The solution is,
PowerPoint Presentation : An engineer is designing the runway for an airport. Of the planes that will use the airport, the lowest acceleration rate is likely to be 3 m/s2. The takeoff speed for this plane will be 65 m/s. assuming this minimum acceleration, what is the minimum allowed length for the runway?
PowerPoint Presentation : A bicyclist traveled from 15.6 m/s to 21.1 m/s over a distance of 30 meters. a. What is the acceleration of the bicyclist? b. How much time does it take the bicyclist to travel the 30 meters?
PowerPoint Presentation : 3. A dragster accelerates to a speed of 112 m/s over a distance of 398 m. Determine the acceleration (assume uniform) of the dragster.
PowerPoint Presentation : 4. An F-15 jet fighter starts from rest and reaches a speed of 330 m/s in 2 seconds. a. What is the planes acceleration? b. How much distance did the jet cover in the 2 seconds? c. How fast was the jet traveling after 1 second?
PowerPoint Presentation : 5. A bullet is fired through a board 10.0 cm thick in such a way that the bullet's line of motion is perpendicular to the face of the board. If the initial speed of the bullet is 400 m/s and it emerges from the other side of the board with a speed of 300 m/s, find (a) The acceleration of the bullet as it passes through the board, and (b) The total time the bullet is in contact with the board.
PowerPoint Presentation : Two teams are competing in swimming relay races. Swimmer A pushes off 2s ahead of swimmer B with 50m left to go. If swimmer A swims at an average speed of 1.9m/s and swimmer B swims at an average speed of 2.1 m/s, who wins the race? How far ahead in seconds and meters is the winner?
PowerPoint Presentation : A cyclist completes 100km race in 2: 25: 30 (hr: min: sec). The race course precedes 50km north, then 25km east, the 25km south. Her split times were 1: 06: 05 at the 50km point and 1: 49: 19 at the 75km point. a. What were her average speeds over the three intervals (50km, 50-75km, 75-100km) how do these speeds compare to her average speed over the whole race? b. What is the displacement from the start to finish? c. What is her average velocity from start to finish? (Both in magnitude and direction) d. at the start of the race the cyclist accelerates from 0 to 15m/s(north) in 7s. What is her average acceleration?
PowerPoint Presentation : A bicyclist traveled from 15.6 m/s to 21.1 m/s over a distance of 30 meters. a. What is the acceleration of the bicyclist? b. How much time does it take the bicyclist to travel the 30 meters?
PowerPoint Presentation : Graphical representation of motion : Motion of a body can e represented by graphs. Types of graphs : Position-time graph Velocity – time graph Acceleration – time graph
PowerPoint Presentation : Position – time graph : Position – y axis time – x axis Significance of the graph p - t: Position of the particle at any instant can be determined. Nature of the motion of the particle can be studied Slope of the graph at any point gives instantaneous of velocity of the body.
PowerPoint Presentation : Determining the Slope :
PowerPoint Presentation : The Meaning of Shape for a p-t Graph : Note that a motion described as a constant, positive velocity results in a line of constant and positive slope when plotted as a position-time graph.
PowerPoint Presentation : consider a car moving with a rightward (+), changing velocity - Note that a motion described as a changing, positive velocity results in a line of changing and positive slope when plotted as a position-time graph.
PowerPoint Presentation : Importance of slope : As the slope goes, so goes the velocity If the velocity is constant, then the slope is constant (i.e., a straight line). If the velocity is changing, then the slope is changing (i.e., a curved line). If the velocity is positive, then the slope is positive (i.e., moving upwards and to the right).
PowerPoint Presentation : Velocity – Time graph : Consider a car moving with a constant, rightward (+) velocity - say of +10 m/s. A car moving with a constant velocity is a car with zero acceleration. Note that a motion described as a constant , positive velocity results in a line of zero slope (a horizontal line has zero slope) when plotted as a velocity-time graph.
PowerPoint Presentation : V-t graph for changing velocity : Consider a car moving with an acceleration 10m/s. Time (s) Velocity (m/s) 0 0 1 10 2 20 3 30 4 40 5 50 The slope of the line is positive, corresponding to the positive acceleration.