Page 1 Chapter 8 Motion Motion – An object that changes its position with respect to time is known to be in motion. Rest – An object is said to be at rest when it does not change its position with respect to time. A reference point is required to describe a motion. For e.g. 1. A car is moving at 60km/hr. It means that the car is moving with respect to its surrounding. The reference point here is the surrounding. 2. A person travelling by a bus. The bus and the person are in motion with respect to the surrounding i.e. the plants, trees road etc. The reference points here are the surroundings. But the person and the bus are at rest with each other because they are moving at same speed and the man always remain at one point inside the bus. The reference point in this case is the bus for the man and vice-a-versa. Motion is a straight line Describing the motion in a straight line – The point from where an object stars moving is treated as its reference point. Distance – the total path length covered by the object from its reference point. Distance only has magnitude (magnitude = numerical value) Displacement – The shortest distance covered by an object from its reference point. Displacement has both magnitude and direction. The shortest distance is always a straight line dram from the reference point to the point of end of the motion. E.g. O A B C 0 20 40 60 km Consider an object moves from point O to C and then comes back to point A Distance covered by the object will be = OC + CA = 60 + 40 = 100 km And Displacement = Shortest distance from the reference point i.e. point O to the end point of end of motion i.e. point A, which is OA Page 2 Chapter 8 Motion Motion – An object that changes its position with respect to time is known to be in motion. Rest – An object is said to be at rest when it does not change its position with respect to time. A reference point is required to describe a motion. For e.g. 1. A car is moving at 60km/hr. It means that the car is moving with respect to its surrounding. The reference point here is the surrounding. 2. A person travelling by a bus. The bus and the person are in motion with respect to the surrounding i.e. the plants, trees road etc. The reference points here are the surroundings. But the person and the bus are at rest with each other because they are moving at same speed and the man always remain at one point inside the bus. The reference point in this case is the bus for the man and vice-a-versa. Motion is a straight line Describing the motion in a straight line – The point from where an object stars moving is treated as its reference point. Distance – the total path length covered by the object from its reference point. Distance only has magnitude (magnitude = numerical value) Displacement – The shortest distance covered by an object from its reference point. Displacement has both magnitude and direction. The shortest distance is always a straight line dram from the reference point to the point of end of the motion. E.g. O A B C 0 20 40 60 km Consider an object moves from point O to C and then comes back to point A Distance covered by the object will be = OC + CA = 60 + 40 = 100 km And Displacement = Shortest distance from the reference point i.e. point O to the end point of end of motion i.e. point A, which is OA Hence, displacement = OA = 20km to the right or west of the reference point Magnitude Direction Uniform motion – An object is said to be in uniform motion when it covers equal distances in equal interval of times. For e.g. A car covered 40km in each hour. Graph for Uniform motion Time (hr) Distance (km) 1 40 2 80 3 120 4 160 5 200 6 240 7 280 Graph 1 – Uniform motion Non – uniform motion – An object is said to be in non-uniform motion when it covers unequal distance in equal intervals of time. For e.g. a man walking in a park. Graph of Non-uniform motion Time (hr) Distance (km) 1 10 2 15 3 17 4 30 5 45 6 80 7 90 1, 40 2, 80 3, 120 4, 160 5, 200 6, 240 7, 280 0 50 100 150 200 250 300 0 1 2 3 4 5 6 7 8 Distance (km) TIme (hr) Distance vs Time Page 3 Chapter 8 Motion Motion – An object that changes its position with respect to time is known to be in motion. Rest – An object is said to be at rest when it does not change its position with respect to time. A reference point is required to describe a motion. For e.g. 1. A car is moving at 60km/hr. It means that the car is moving with respect to its surrounding. The reference point here is the surrounding. 2. A person travelling by a bus. The bus and the person are in motion with respect to the surrounding i.e. the plants, trees road etc. The reference points here are the surroundings. But the person and the bus are at rest with each other because they are moving at same speed and the man always remain at one point inside the bus. The reference point in this case is the bus for the man and vice-a-versa. Motion is a straight line Describing the motion in a straight line – The point from where an object stars moving is treated as its reference point. Distance – the total path length covered by the object from its reference point. Distance only has magnitude (magnitude = numerical value) Displacement – The shortest distance covered by an object from its reference point. Displacement has both magnitude and direction. The shortest distance is always a straight line dram from the reference point to the point of end of the motion. E.g. O A B C 0 20 40 60 km Consider an object moves from point O to C and then comes back to point A Distance covered by the object will be = OC + CA = 60 + 40 = 100 km And Displacement = Shortest distance from the reference point i.e. point O to the end point of end of motion i.e. point A, which is OA Hence, displacement = OA = 20km to the right or west of the reference point Magnitude Direction Uniform motion – An object is said to be in uniform motion when it covers equal distances in equal interval of times. For e.g. A car covered 40km in each hour. Graph for Uniform motion Time (hr) Distance (km) 1 40 2 80 3 120 4 160 5 200 6 240 7 280 Graph 1 – Uniform motion Non – uniform motion – An object is said to be in non-uniform motion when it covers unequal distance in equal intervals of time. For e.g. a man walking in a park. Graph of Non-uniform motion Time (hr) Distance (km) 1 10 2 15 3 17 4 30 5 45 6 80 7 90 1, 40 2, 80 3, 120 4, 160 5, 200 6, 240 7, 280 0 50 100 150 200 250 300 0 1 2 3 4 5 6 7 8 Distance (km) TIme (hr) Distance vs Time Graph 2 – Non-uniform motion Speed and Velocity Speed – Distance covered per unit time is called speed Average speed = Total distance covered Total time taken v = s t where v = speed s = distance travelled t = time taken Velocity – Speed with direction is called velocity Displacement per unit time is called velocity Direction of velocity is same as the direction of displacement or motion. v = displacement time taken Average velocity = initial velocity + final velocity 2 vav = µ + v 2 where µ = initial velocity v = final velocity 1, 10 2, 15 3, 17 4, 30 5, 45 6, 80 7, 90 0 10 20 30 40 50 60 70 80 90 100 0 1 2 3 4 5 6 7 8 Distace (km) Time (hr) Distance vs time Page 4 Chapter 8 Motion Motion – An object that changes its position with respect to time is known to be in motion. Rest – An object is said to be at rest when it does not change its position with respect to time. A reference point is required to describe a motion. For e.g. 1. A car is moving at 60km/hr. It means that the car is moving with respect to its surrounding. The reference point here is the surrounding. 2. A person travelling by a bus. The bus and the person are in motion with respect to the surrounding i.e. the plants, trees road etc. The reference points here are the surroundings. But the person and the bus are at rest with each other because they are moving at same speed and the man always remain at one point inside the bus. The reference point in this case is the bus for the man and vice-a-versa. Motion is a straight line Describing the motion in a straight line – The point from where an object stars moving is treated as its reference point. Distance – the total path length covered by the object from its reference point. Distance only has magnitude (magnitude = numerical value) Displacement – The shortest distance covered by an object from its reference point. Displacement has both magnitude and direction. The shortest distance is always a straight line dram from the reference point to the point of end of the motion. E.g. O A B C 0 20 40 60 km Consider an object moves from point O to C and then comes back to point A Distance covered by the object will be = OC + CA = 60 + 40 = 100 km And Displacement = Shortest distance from the reference point i.e. point O to the end point of end of motion i.e. point A, which is OA Hence, displacement = OA = 20km to the right or west of the reference point Magnitude Direction Uniform motion – An object is said to be in uniform motion when it covers equal distances in equal interval of times. For e.g. A car covered 40km in each hour. Graph for Uniform motion Time (hr) Distance (km) 1 40 2 80 3 120 4 160 5 200 6 240 7 280 Graph 1 – Uniform motion Non – uniform motion – An object is said to be in non-uniform motion when it covers unequal distance in equal intervals of time. For e.g. a man walking in a park. Graph of Non-uniform motion Time (hr) Distance (km) 1 10 2 15 3 17 4 30 5 45 6 80 7 90 1, 40 2, 80 3, 120 4, 160 5, 200 6, 240 7, 280 0 50 100 150 200 250 300 0 1 2 3 4 5 6 7 8 Distance (km) TIme (hr) Distance vs Time Graph 2 – Non-uniform motion Speed and Velocity Speed – Distance covered per unit time is called speed Average speed = Total distance covered Total time taken v = s t where v = speed s = distance travelled t = time taken Velocity – Speed with direction is called velocity Displacement per unit time is called velocity Direction of velocity is same as the direction of displacement or motion. v = displacement time taken Average velocity = initial velocity + final velocity 2 vav = µ + v 2 where µ = initial velocity v = final velocity 1, 10 2, 15 3, 17 4, 30 5, 45 6, 80 7, 90 0 10 20 30 40 50 60 70 80 90 100 0 1 2 3 4 5 6 7 8 Distace (km) Time (hr) Distance vs time Time (hr) Distance (km) 1 40 2 80 3 120 4 160 5 200 6 240 7 280 Graph 3 - Distance vs Time at constant velocity Acceleration – The rate of change of velocity is known as acceleration Acceleration = Change in velocity Time taken a = v - µ t v = final velocity µ = initial velocity t = time taken Graph Time (min) Velocity (km/hr) 1 10 2 20 3 30 4 40 5 50 6 60 7 70 1, 40 2, 80 3, 120 4, 160 5, 200 6, 240 7, 280 0 50 100 150 200 250 300 0 1 2 3 4 5 6 7 8 Distance (km) Time (hr) Distance vs Time Page 5 Chapter 8 Motion Motion – An object that changes its position with respect to time is known to be in motion. Rest – An object is said to be at rest when it does not change its position with respect to time. A reference point is required to describe a motion. For e.g. 1. A car is moving at 60km/hr. It means that the car is moving with respect to its surrounding. The reference point here is the surrounding. 2. A person travelling by a bus. The bus and the person are in motion with respect to the surrounding i.e. the plants, trees road etc. The reference points here are the surroundings. But the person and the bus are at rest with each other because they are moving at same speed and the man always remain at one point inside the bus. The reference point in this case is the bus for the man and vice-a-versa. Motion is a straight line Describing the motion in a straight line – The point from where an object stars moving is treated as its reference point. Distance – the total path length covered by the object from its reference point. Distance only has magnitude (magnitude = numerical value) Displacement – The shortest distance covered by an object from its reference point. Displacement has both magnitude and direction. The shortest distance is always a straight line dram from the reference point to the point of end of the motion. E.g. O A B C 0 20 40 60 km Consider an object moves from point O to C and then comes back to point A Distance covered by the object will be = OC + CA = 60 + 40 = 100 km And Displacement = Shortest distance from the reference point i.e. point O to the end point of end of motion i.e. point A, which is OA Hence, displacement = OA = 20km to the right or west of the reference point Magnitude Direction Uniform motion – An object is said to be in uniform motion when it covers equal distances in equal interval of times. For e.g. A car covered 40km in each hour. Graph for Uniform motion Time (hr) Distance (km) 1 40 2 80 3 120 4 160 5 200 6 240 7 280 Graph 1 – Uniform motion Non – uniform motion – An object is said to be in non-uniform motion when it covers unequal distance in equal intervals of time. For e.g. a man walking in a park. Graph of Non-uniform motion Time (hr) Distance (km) 1 10 2 15 3 17 4 30 5 45 6 80 7 90 1, 40 2, 80 3, 120 4, 160 5, 200 6, 240 7, 280 0 50 100 150 200 250 300 0 1 2 3 4 5 6 7 8 Distance (km) TIme (hr) Distance vs Time Graph 2 – Non-uniform motion Speed and Velocity Speed – Distance covered per unit time is called speed Average speed = Total distance covered Total time taken v = s t where v = speed s = distance travelled t = time taken Velocity – Speed with direction is called velocity Displacement per unit time is called velocity Direction of velocity is same as the direction of displacement or motion. v = displacement time taken Average velocity = initial velocity + final velocity 2 vav = µ + v 2 where µ = initial velocity v = final velocity 1, 10 2, 15 3, 17 4, 30 5, 45 6, 80 7, 90 0 10 20 30 40 50 60 70 80 90 100 0 1 2 3 4 5 6 7 8 Distace (km) Time (hr) Distance vs time Time (hr) Distance (km) 1 40 2 80 3 120 4 160 5 200 6 240 7 280 Graph 3 - Distance vs Time at constant velocity Acceleration – The rate of change of velocity is known as acceleration Acceleration = Change in velocity Time taken a = v - µ t v = final velocity µ = initial velocity t = time taken Graph Time (min) Velocity (km/hr) 1 10 2 20 3 30 4 40 5 50 6 60 7 70 1, 40 2, 80 3, 120 4, 160 5, 200 6, 240 7, 280 0 50 100 150 200 250 300 0 1 2 3 4 5 6 7 8 Distance (km) Time (hr) Distance vs Time Graph 4 - Velocity vs Time at uniform acceleration The area under two points in a velocity time graph gives distance covered in that time The distance between time interval D (3hr) and C (5hr) is given by the area of the trapezium ABCD Area of trapezium = ½(b 1 + b2)*h Area of trapezium = ½(AD + BC)*h = ½*(30+50)*2 (height = 5 – 3 (time period)) = ½(80)*2 = 80km But if the object moves with constant velocity and there is no acceleration Same velocity at all time Velocity vs time graph at zero acceleration 1, 40 2, 40 3, 40 4, 40 5, 40 6, 40 0 5 10 15 20 25 30 35 40 45 0 1 2 3 4 5 6 7 Velocity (km/hr) Time (hr) Velocity vs time 1, 10 2, 20 3, 30 4, 40 5, 50 6, 60 7, 70 0 10 20 30 40 50 60 70 80 0 1 2 3 4 5 6 7 8 Velocity km/hr TIme (min) Velocity vs time A B C DRead More

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