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MOTION: MOTION π Motion :- is the change in position of a body with time. Motion can be described in terms of the distance moved or the displacement. π Distance moved :- is the actual length of the path travelled by a body. π Displacement :- is the length of the shortest path travelled by a body from its initial position to its final position. π Eg :- If a body starts moving in a straight line from origin O and moves through C and B and reaches A and then moves back and reaches C through B, then π Distance travelled = 60 + 35 = 95 km π Displacement = 25 km O C B A 0 5 10 15 20 25 30 35 40 45 50 55 60 km What is a Motion?
Slide3: Vector and Scalar π A vector quantity is characterized by having both a magnitude and a direction. π Displacement, Velocity, Acceleration, Force β¦ π Denoted in boldface type or with an arrow over the π π top . π A scalar quantity has magnitude, but no direction. π Distance, Mass, Temperature, Time β¦ π For motion along a straight line, the direction is represented simply by + and β signs. π + sign: Right or Up. π - sign: Left or Down. π 1-D motion can be thought of as a component of 2-D and 3-D motions.
Slide4: Velocity π V elocity is the rate of change of position. π Velocity is a vector quantity. π Velocity has both magnitude and direction. π Velocity has a unit of [length/time]: meter/second. π We will be concerned with three quantities, defined as: π Average velocity π Average speed π Magnitude β the speed of the object π Direction β the direction the object is moving displacement distance
Uniform Velocity: π Uniform velocity is the special case of constant velocity π In this case, instantaneous velocities are always the same, all the instantaneous velocities will also equal the average velocity π Begin with then Uniform Velocity x x(t) t 0 x i x f v v(t) t 0 t f v x t i Note: we are plotting velocity vs. time
What is Speed?: What is Speed? π Speed is the distance traveled divided by the time interval during which the motion occurred π Normally, objects do not travel at a constant speed π Average Speed - Total distance Total time
Acceleration: Acceleration π Acceleration is the rate at which velocity changes over time π An object accelerates if its speed, direction, or both change π Average acceleration = final velocity β starting velocity time it takes to change velocity
Average Acceleration: Average Acceleration π Changing velocity (non-uniform) means an acceleration is present. π Acceleration is the rate of change of velocity. π Acceleration is a vector quantity. π Acceleration has both magnitude and direction. π Acceleration has a dimensions of length/time 2 : [m/s 2 ]. π Definition: π Average acceleration π Instantaneous acceleration
Uniform motion and Non uniform motion :-: Uniform motion and Non uniform motion :- π Uniform motion :- If a body travels equal distances in equal intervals of time, it is said to be in uniform motion. π Non uniform motion :- If a body travels unequal distances in equal intervals of time, it is said to be in non uniform motion. π Speed :- of a body is the distance travelled by the body in unit time. Distance = Speed Time If a body travels a distance s in time t then its speed V= S T The SI unit of speed is metre per second m / s or ms - 1 Since speed has only magnitude it is a scalar quantity. π Average speed :- is the ratio of the total distance travelled to the total time taken. Average speed= Total distance travelled Total time taken
Speed with direction :- : Speed with direction :- π The rate of motion of a body is more meaningful if we specify its direction of motion along with speed. The quantity which specifies both the direction of motion and speed is velocity. π Velocity :- of a body is the displacement of the body per unit time. Displacement Velocity = Time taken Since velocity has both magnitude and direction, it is a vector quantity. π Average velocity :- is the ratio of the total displacement to the total time taken. Total displacement Average velocity = Total time taken Average velocity is also the mean of the initial velocity u and final velocity v. Initial velocity + Final velocity u + v Average velocity = av = 2 2 π Speed and velocity have the same units m / s or ms -1
Rate of change of velocity :-: Rate of change of velocity :- π During uniform motion of a body in a straight line the velocity remains constant with time. In this case the change in velocity at any time interval is zero ( no change in velocity). π During non uniform motion the velocity changes with time. In this case the change in velocity at any time interval is not zero. It may be positive (+ ve ) or negative (- ve ). The quantity which specifies changes in velocity is acceleration. π Acceleration :- is the change in velocity of a body per unit time.( or the rate of change of velocity.) Change in velocity Acceleration = Time If the velocity of a body changes from initial value u to final value v in time t, then acceleration a is v - u a = t π The SI unit of acceleration is ms - 2 π Uniform acceleration :- If the change in velocity is equal in equal intervals of time it is uniform acceleration. π Non uniform acceleration :- If the change in velocity is unequal in equal intervals of time it is non uniform acceleration.
Graphical representation of motion :-: Graphical representation of motion :- A B 10 20 30 t 1 t 2 s 1 s 2 C Time (s) Distance (m) X Y 5 10 15 20 Distance β time graph for a body moving with uniform speed 0 π Distance β Time graphs :- The change in the position of a body with time can be represented on the distance time graph. In this graph distance is taken on the y β axis and time is taken on the x β axis. π The distance time graph for uniform speed is a straight line ( linear ). This is because in uniform speed a body travels equal distances in equal intervals of time. π We can determine the speed of the body from the distance β time graph. For the speed of the body between the points A and B, distance is (s 2 β s 1 ) and time is (t 2 β t 1 ). s (s 2 β s 1 ) v = ---- v = ----------- t (t 2 β t 1 ) 20 β 10 10 = --------- = ---- 10 β 5 5 = 2 ms -1
Slide13: π The distance β time graph for non uniform motion is non linear. This is because in non uniform speed a body travels unequal distances in equal intervals of time. 20 40 Time (s) Distance (m) X 10 30 5 0 10 15 20 Distance β time graph for a body moving with non uniform speed Y
Velocity β time graphs :-: Velocity β time graphs :- π The change in the velocity of a body with time can be represented on the velocity time graph. In this graph velocity is taken on the y β axis and time is taken on the x β axis. π If a body moves with uniform velocity, the graph will be a straight line parallel to the x β axis . This is because the velocity does not change with time. π To determine the distance travelled by the body between the points A and B with velocity 20 km h -1 s v = --- t s = v x t v = 20 km h -1 = AC or BD t = t 2 β t 1 = DC = AC (t 2 β t 1 ) s = AC X CD s = area of the rectangle ABDC Velocity β time graph for a body moving with uniform velocity 20 40 Time (s) Velocity (km h -1 ) X 10 30 5 0 10 15 20 t 1 t 2 A B C D Y
Velocity β time graphs :-: π If a body whose velocity is increasing with time, the graph is a straight line having an increasing slope. This is because the velocity increases by equal amounts with equal intervals of time. The area under the velocity β time graph is the distance (magnitude of displacement) of the body. The distance travelled by a body between the points A and E is the area ABCDE under the velocity β time graph. s = area ABCDE = area of rectangle ABCD + area of triangle ADE 1 s = AB X BC + --- ( AD X DE ) 2 A B 10 20 30 t 1 t 2 C Time (s) Velocity (m s -1 ) X Y 10 20 30 40 Velocity β time graph for a body moving with uniform acceleration D E 0 Velocity β time graphs :-
Slide16: π If a body whose velocity is decreasing with time, the graph is a straight line having an decreasing slope. This is because the velocity decreases by equal amounts with equal intervals of time. iv) If a body whose velocity is non uniform, the graph shows different variations. This is because the velocity changes by unequal amounts in equal intervals of time. 20 40 Time (s) Velocity (ms -1 ) X 10 30 5 0 10 15 20 20 40 Time (s) Velocity (ms -1 ) X 10 30 5 0 10 15 20 Velocity β time graph for a uniformly decelerated motion Velocity β time graph for non uniform acceleration Y Y
Equations of motions by graphical method :-: Equations of motions by graphical method :- The motion of a body moving with uniform acceleration can be described with the help of three equations called equations of motion. The equations of motion are :- i ) v = u + at ii) s = ut + ½ at 2 iii) 2as = v 2 β u 2 where u - is the initial velocity v - is the final velocity a - is acceleration t - is the time s - is the distance traveled
Equation for velocity β time relation ( v = u + at ) :-: Equation for velocity β time relation ( v = u + at ) :- π Consider a velocity β time graph for a body moving with uniform acceleration βaβ. The initial velocity is u at A and final velocity is v at B in time t. π Perpendicular lines BC and BE are drawn from point B to the time and velocity axes so that the initial velocity is OA and final velocity is BC and time interval is OC. Draw AD parallel to OC. π We observe that π BC = BD + DC = BD + OA π Substituting BC = v and OA = u We get v = BD + u or BD = v - u Change in velocity Acceleration = --------------------------- Time BD BD v - u a = ----- = ----- or a = --------- AD OC t v β u = at or v = u + at Time (s) Velocity (ms -1 ) X O Velocity β time graph for a uniformly accelerated motion Y t u v A B C D E
Equation for position β time relation (s = ut + ½ at2 ) :-: Equation for position β time relation (s = ut + ½ at 2 ) :- π Consider a velocity β time graph for a body moving with uniform acceleration βaβ travelled a distance s in time t. π The distance traveled by the body between the points A and B is the area OABC. s = area OABC ( which is a trapezium ) = area of rectangle OABC + area of triangle ABD 1 = OA X OC + --- ( AD X BD ) 2 Substituting OA = u, OC = AD = t, BD = v β u = at We get 1 s = u x t + -- ( t x at ) 2 or s = ut + ½ at 2 Time (s) Velocity (ms -1 ) O Velocity β time graph for a uniformly accelerated motion t u v A B C D E
Equation for position β velocity relation (2as = v2 βu2) :-: Equation for position β velocity relation ( 2as = v 2 βu 2 ) :- π Consider a velocity β time graph for a body moving with uniform acceleration βaβ travelled a distance s in time t. The distance travelled by the body between the points A and B is the area OABC. s = area of trapezium OABC (OA + BC) X OC s = ---------------------- 2 Substituting OA = u, BC = v and OC = t ( u + v ) X t We get s = ----------------- 2 From velocity β time relation ( v β u ) t = ----------- a ( v + u ) X ( v β u ) s = ----------------------- or 2as = v 2 β u 2 2a Time (s) Velocity (ms -1 ) O Velocity β time graph for a uniformly accelerated motion t u v A B C D E
Slide21: Circular motion :- π The motion of a body in a circular path is called circular motion. π Uniform circular motion :- If a body moves in a circular path with uniform speed, its motion is called uniform circular motion. π Uniform circular motion is accelerated motion because in a circular motion a body continuously changes its direction. π The circumference of a circle of radius r is given by 2 Π» r. If a body takes time t to go once around the circular path, then the velocity v is given by 2 Π» r π v = ---- t
Problem-Solving Hints: Problem-Solving Hints π Read the problem π Draw a diagram π Choose a coordinate system, label initial and final points, indicate a positive direction for velocities and accelerations π Label all quantities, be sure all the units are consistent π Convert if necessary π Choose the appropriate kinematic equation π Solve for the unknowns π You may have to solve two equations for two unknowns π Check your results
A Numerical is here for you!!!!!!!!!: π Farmer Jones drives 6 miles down a straight road. She turns around and drives 4 miles back. What was her average speed for this trip if it took 1 hour? A Numerical is here for you!!!!!!!!! 6 Miles 4 Miles
Your answer to this problem depends on your interpretation of "distance traveled". You could say:: Your answer to this problem depends on your interpretation of "distance traveled". You could say: π The total distance traveled by Farmer Jones is 10 miles. Therefore her average speed is 10 mi/hr. π The net distance traveled by Farmer Jones is 2 miles. Therefore, her average speed is 2 mi/hr. π There are good reasons to use either interpretation - it's mostly a matter of preference. We will interpret "distance traveled" to be net distance ( also called displacement). Farmer Jones' average speed was 2 mi/hr.
Thank You: Thank You π Created By-Harsh Arora π Class-9D π Roll no.18 π Subject-Physics π Topic-Motion