Motion

1. Motion

2. What is motion? • Motion is nothing,but movement. • When do you say that you are moving? • If you are standing in a particular place, are you in movement? • If you are walking from your home to school? • You are changing your position with time. • Therefore, a body is said to be in motion if it changes its position with time. • Eg: Moving blades of a fan. • Motion of a car.

3. Difference between fast and slow motion • Fast motion can be observed easily. • Eg:second’s hand of a watch. • The slow motion is difficult to be observed immediately. • Eg:Minute hand and Hour hand of a watch.

4. Motion is a relative term • Motion of an object is always with respect to some frame of reference. • What is called Frame of reference? • Suppose a person is standing in a bus stop with two kids.Are they in motion? • Suppose a bus is passing through the road in front of them. • Is the bus in motion? • Suppose there are 2 passengers A and B inside the bus. • Is the A in motion according to B? • Is the B in motion according to A? • Is the A and B in motion according to the people standing in the bus stop?

5. Motion is a relative term • A person is at rest or in motion depending on the person who is observing it. • So Frame of Reference is the reference frame of the observer. • With one frame of Reference,the object may be at rest;whereas with some other frame of Reference, the object may be in motion.

6. Basic Types of motion • Rectilinear Motion. • Motion in a Straight Line. • Circular Motion • Motion along a circular path.

7. Describing motion of an object • In order to describe the motion,position needs to be defined. • Position:The point at which the object is located at a particular instant of time. • Suppose a boy is riding the cycle from point A to point B. • A is one position and B is another position. • If the position of the cycle changes from point A to point B,then the cycle is in motion.

8. Distinguish between Distance travelled and Displacement Distance travelled Displacement • The actual length of the path covered by a moving body irrespective of the direction in which the body travels. • Scalar quantity • The straight line path between the initial and final position of a body in motion. • It is the shortest distance between the initial and final position of the body,along with direction. • Vector quantity

9. Distinguish between scalar and vector quantities. • Scalar:The quantity having only magnitude and no specified direction. • Magnitude- size of the quantity. • Eg:Pathlength,speed • Hari-------------------------10km • Vector:The quantity having both magnitude and direction. • Eg:Displacement ,velocity • Hari-----------------------------10km towards east.

10. case 1 Initial position=Home Final position-Mc donald’s Distance-? Displacement-?

11. Case 2 When path length=Displacement.

12. Case 3 • What happens when Raju travels from home,reacheschurch,Mcdonald and come back to home. • Distance travelled= • Displacement=

13. Uniform and Non-uniform motion • A body is said to be in uniform motion if it travels equal distances in equal intervals of time. • For Eg. ,a car running at a constant speed of 10m/s will cover equal distances of 10m ,every second,so its motion is uniform. • A body is said to be in Non-uniform motion if it covers unequal distances in equal intervals of time. • Eg: 4.9m in the first second,14.7m in the second second, 24.5m in the third second and so on…. • Eg: Motion of a freely falling body.,Motion of the train starting from a railway station.Non-uniform motion is also called accelerated motion.

16. Speed • If a car is running slow, speed is low. • If a car is running fast, speed is high. • Thus ,the speed of a moving body gives us an idea of how slow or fast the body is moving. • Definition: • Speed of a body is the distance travelled by it per unit time. • It can be calculated by dividing the Distance travelled by the Time taken to travel this distance. • Speed=Distance Travelled /Time Taken. • v=s/t. s-Distance travelled.t-time taken. v-speed.

17. Speed • The S.I unit of speed is m/sec. • Other units are cm/s,Km/h. • Speed has magnitude only,no specified direction. • So it is a scalar quantity. • Speedometer- To measure speed of a car. • Odometer-To measure the distance travelled by the car.

18. Velocity • Velocity of a body is the distance travelled by it per unit time in a given direction. • Velocity=Distance travelled in a given direction/Time taken.=Displacement/Time taken • v=s/t,where v is the velocity,s is the displacement and t-time taken • S.I unit-m/s. • Other units are cm/s ,km/hr. • It is a vector quantity. • The direction of velocity is the same as the direction of displacement.

19. Distinguish between speed and velocity • Speed:Rate at which an object covers distance. • Scalar. • Velocity:Rate at which an object changes its position. • vector

20. What is speed and velocity for this case? Speed- velocity

21. What is speed and velocity for this case? What if Raju travels from home to mcdonalds and come back to home?speed-? Velocity-?

22. Average speed • In Non-uniform motion, the rate of motion of objects ar e described in terms of Average speed. • It is the measure of total distance covered in a given time. • The Average speed of an object is obtained by dividing the total distance travelled by the total time taken.That is • Average speed =Total distance travelled /Total time taken. • V=s/t. • There is no difference between speed and Average speed definition wise.

23. Analysis of Average speed for uniform and Non-uniform motion • Uniform motion: • Suppose a car is travelling 20 km in 1 hr. • The speed and Average speed will be the same; 20 km/hr. • Non-uniform motion: • The speed of the vehicle is low in the beginning; then it increases and then it increases a lot.speed of the vehicle is changing from one point to another. • Suppose a car is moving from A toB with an Average speed of 5 km/h, from B to C with an Average speed of 6 km/hr; but the average speed of the journey from A to C is not 11 km/h.It will be equal to • Total distance travelled/Total time taken.

24. Average and Instantaneous speed • Average speed : Measure of total distance covered in a given time. • Instantaneous speed : Measure of distance covered at every instant of time.

25. Average velocity • It is the measure of the total displacement of the body in a given direction. • Average velocity= Total Displacement/ Total time taken.

26. Acceleration • A cceleration of a body is the rate of change of its velocity with time. • Acceleration=change in velocity/Time taken. • Change in velocity=v-u • Therefore, a=v-u/t. • S.I unit: m/s2 • Other units are cm/s2 and km/h2 • If the motion is in a straight line, the acceleration is in the direction of velocity, so it is a vector quantity. • When a body is moving with uniform velocity, the acceleration is zero. • When the velocity of a body is not uniform, the motion is accelerated.

27. Uniform Acceleration • A body has a uniform acceleration if it travels in a straight line and its velocity increases by equal amounts in equal intervals of time. • A body has a uniform acceleration if its velocity changes at a uniform rate. • Eg: Motion of a freely falling body • Ball rolling down an inclined plane.

28. Non-uniform Acceleration • A body has a non-uniform acceleration if its velocity increases by unequal amounts in equal intervals of time. • A body has a non-uniform acceleration if its velocity changes at a non-uniform rate. • Eg: the movement of a car on a crowded city road.

29. Retardation or Deceleration • Acceleration is of two types: Positive and Negative. • If the velocity of the body increases,then the acceleration is positive. • If the velocity of the body decreases,then the acceleration is negative. • Decrease in the velocity of the body is known as Retardation or Deceleration. • It is actually acceleration with a negative sign.

30. Average velocity • When an object is moving along a straight line at a variable speed,the magnitude of the rate of motion is expressed in terms of average velocity. • It is given by the arithmetic mean of initial velocity and final velocity for a given period of time. That is, • Average velocity= Initial velocity+Final velocity/2 • Mathematically, • v av =u+v/2.

31. Graphical Representation of Motion • Graphs can be used to calculate speed, Acceleration and Distance travelled by a body. • In the drawing of Graphs, the terms velocity and speed are used in the same sense. • There are two types of Graphs: • a) Distance- Time Graphs, with Distance along the y-axis and Time along the y-axis. • B) Velocity- Time Graphs,with velocity along the y-axis and Time along the X-axis.

32. Distance-Time Graphs • A body with uniform speed travels equal distances in equal intervals of time,ie, Distance travelled is directly proportional to Time. • So the graph will be a straight line.

33. Distance- Time Graph for a body with uniform speed The straight line graph between Distance and Time tells us that the body is moving with uniform speed.

34. Distance-Time Graph to calculate speed • Speed can be calculated from the Distance -Time graph by drawing a slope in the graph. • How to draw a slope: • Drop a perpendicular AB on the time axis OB. • AB - represents Distance Travelled. • OB-represents Time taken • AB/OB is known as the slope of the graph

35. Speed from the slope The slope of a Distance- Time Graph indicate speed.so A Distance- Time Graph can be used to find the speed of the body.

36. Distance –Time Graph for Non-uniform motion • It is a curved line. • Then its speed is non-uniform.

37. Distance- Time graph for non-uniform motion When a body moves with non-uniform speed,then its motion is said to be accelerated. The curved line also represents the Distance-Time Graph of a body moving with accelerated motion

38. Note: • If Displacement-Time Graph or Position-Time Graph is drawn, then it will specifically represent velocity. • Straight line Graph- uniform velocity.

39. Case 3 The Graph shows that the body is at rest

42. Velocity –Time Graph or Speed –Time Graph • There are three types of speed-Time Graphs for a moving body.They are: • 1) when the speed of the body remains constant. ( and there is no acceleration) • 2)When the speed of a body changes at a uniform rate (there is uniform acceleration.) • 3) When the speed of the body changes in a non-uniform way (there is non-uniform acceleration)

43. Speed-Time Graph when the speed remains constant The speed does not change with time and there is no acceleration.This is the graph for a body moving with constant speed.

44. case1 • This graph shows that the velocity is constant. • Here ,as time increases,the velocity is not changing.

46. Speed-Time Graph when speed changes at a uniform rate • The speed-Time graph for uniform acceleration is a straight line. This graph shows that as time increases,velocity also increases. • That is,the body is having an acceleration. • This is uniformly accelerated motion. • We can use the speed-Time Graph to find the acceleration ( By finding the slope ) and The Distance travelled ( By finding the area enclosed.)

47. Speed-Time Graph when speed changes at a Non-uniform rate The graph is a curved line.. It can have any shape based on the fact that the velocity is increasing or decreasing.

49. To find out the value of Acceleration from the speed -Time graph • Draw a perpendicular from a particular time point Q in the time axis to touch the straight line at point P. O is the origin. R be the corresponding point of p on the y-axis. • Acceleration=change in speed/ Time taken. • Change in speed= PQ • Time taken=OQ. • Therefore, Acceleration a =PQ/OQ. • That is ,the slope of a speed-Time graph in uniform rate gives the acceleration

50. How to Find Distance travelled from Speed- Time Graph • Draw a perpendicular at the point C which meets the straight line graph at point B. • Speed at C=CB . • CB=OA. • Thus , speed at C= OA. • Time at C=OC. • Distance travelled = Speed x Time taken. • From the Graph, Distance travelled =OAxOC • Distance travelled= Area of the rectangle OABC. • Thus,in a speed-Time graph,the area enclosed by the speed-time graph and the time axis gives the distance travelled by the body.