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PHYSICS MOTION, , Motion, Rest and Motion, , , , , If the position of an object does not change as time passes, then it is said to be at rest. If the position, of an object changes as time passes, then it is said to be in motion., An object can be at rest with respect to one thing and in motion with respect to some other thing at the, same time. So, the states of rest and motion are relative only., To locate the position of an object, we have to choose some suitable reference point called the, origin., , Distance and Displacement, , , , , , , , The distance travelled by an object is the length of the actual path traversed by the object during, motion. It is a scalar quantity., The displacement of an object in motion is the shortest distance between the initial position and the, final position of the object. It is a vector quantity., , The distance travelled by an object in motion can never be zero or negative., The displacement of an object can be positive, zero or negative. Never can the distance travelled be, less than the displacement., Both distance and displacement have the same units., , www.topperlearning.com, , 2

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PHYSICS MOTION, , Uniform and Non-uniform Motion, , Uniform motion, Motion, Non-uniform, motion, , , , , An object is said to be in uniform motion if it travels equal distances in equal intervals of time,, howsoever small the intervals may be., An object is said to have non-uniform motion if it travels unequal distances in equal intervals of time., , Speed, , , , , , , , , Speed of a body is defined as the distance travelled by the body in unit time. The SI unit of speed is, metre/second (m/s)., Distance travelled, Speed, Time taken, s, If ‘s’ is the distance travelled by a body in time ‘t’, then its speed ‘v’ is given as v, t, Speed of a body is a scalar quantity. It can be zero or positive but can never be negative., If a body covers equal distances in equal time intervals, howsoever small the intervals may be, then it, is said to have uniform speed (or constant speed)., If a body covers unequal distances in equal time intervals, however small the intervals may be, then it, is said to have non-uniform speed (or variable speed)., For bodies moving with non-uniform speed, we describe the rate of motion in terms of their average, speed., Total distance travelled, Average speed=, Total time taken, , www.topperlearning.com, , 3

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PHYSICS MOTION, , Velocity, , , , , Velocity of a body is defined as the distance travelled by the body in unit time in a given direction., The SI unit of velocity is the same as that of speed, i.e. metre/second (m/s)., Distance travelled in a given direction, Velocity, Time taken, or, Velocity, , i.e. v, , , , , , , , Displacement, Time taken, , s, t, , where v is velocity and s is displacement of the body in time t., Velocity of a body is a vector quantity. It can be positive, negative or zero., A body is said to be moving with uniform velocity (or constant velocity) if it travels along a straight, line, covering equal distances in equal intervals of time, howsoever small these intervals may be., A body is said to be moving with non-uniform velocity (or variable velocity) if it covers unequal, distances in a particular direction in equal intervals of time or if the direction of motion of the body, changes., When the velocity of a body is changing at a uniform rate over a period of time, the average velocity, for that time period is given by the arithmetic mean of the initial and final velocity of the body., Average velocity, or, , v av, , Initial velocity + Final velocity, 2, u v, 2, , where ‘u’ is initial velocity, ‘v’ is final velocity and v av is average velocity., , www.topperlearning.com, , 4

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PHYSICS MOTION, , Acceleration, , , Acceleration of a body is defined as the rate of change of its velocity with time., Acceleration, , or, a, , , , , , , , Change in velocity, Time taken, Final velocity - Initial velocity, Time taken, v -u, t, , where ‘u’ is initial velocity, ‘v’ is final velocity, ‘a’ is acceleration of the body and ‘t’ is time taken for, change in velocity., Acceleration is a vector quantity. It can be positive, negative or zero. The SI unit of acceleration is, metre per second square (m/s2)., If the velocity of a body increases, then the acceleration is positive. If the velocity of a body decreases,, then the acceleration is negative. Negative acceleration is called retardation., If acceleration occurs in the direction of velocity, then it is taken as positive and negative when it is, opposite to the direction of velocity., A body is said to possess uniform acceleration if it travels in a straight line and its velocity increases, or decreases by equal amounts in equal intervals of time., A body is said to possess non-uniform acceleration if its velocity changes by unequal amounts in, equal intervals of time., , Distance–Time Graph, , , The distance–time graph of a body moving with uniform speed is a straight line., , , , Speed of a body can be obtained from the slope of the distance–time graph., , www.topperlearning.com, , 5

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PHYSICS MOTION, , , Let s1 and s2 be the distance travelled by the object in time t1 and t2, respectively. Here (s2 – s1) gives, the distance travelled by the body in time interval (t2 – t1)., Distance travelled, Speed, Time taken, s2 s1, v, t 2 t1, , , , The distance–time graph of a body moving with non-uniform speed is a curved line with a variable, slope indicating variable speed., , Velocity–Time Graph, , , The velocity–time graph of a body moving with uniform velocity is a straight line parallel to the time, axis., , , , The magnitude of displacement or distance travelled by the body is equal to the area enclosed by, the velocity–time graph and time axis., Distance travelled = Speed × Time taken, = OA × OC, = Area of rectangle OABC, , www.topperlearning.com, , 6

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PHYSICS MOTION, , , The velocity–time graph of a body moving with uniform acceleration is a straight line inclined to the, time axis., , o The slope of the velocity–time graph represents the acceleration of the body., Change in speed ED, Acceleration, Time taken, AD, o The area enclosed by the velocity–time graph and time axis gives the distance travelled by, the body., Distance travelled = Area of ABCDE, = Area of triangle ADE+ Area of rectangle ABCD, =, , , , 1, 2, , AD DE + AB BC, , The velocity–time graph of a body moving with non-uniform acceleration can have any shape,, indicating variable speed., , www.topperlearning.com, , 7

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PHYSICS MOTION, , Equations of Motion, , , , The three equations of motion of a body moving along a straight line with uniform acceleration are, , v = u + at, , s = ut + (1/2) at2, , v2 - u2 = 2as, , where ‘u’ is initial velocity of the body which moves with uniform acceleration ‘a’ for time t, ‘v’ is, final velocity and ‘s’ is distance travelled by the body in time t., , Uniform Circular Motion, , , , , , , When a body moves along a circular path with a uniform speed, its motion is called uniform circular, motion., Examples: Motion of the Moon around the Earth, a cyclist moving in a circular track at constant speed, In uniform circular motion, although the speed remains constant, the direction of motion and velocity, change continuously. Thus, uniform circular motion is an accelerated motion., The external force needed to make a body travel in a circular path is known as centripetal force., The circumference of a circle of radius ‘r’ is given by 2r. If a body takes ‘t’ seconds to go once round, 2πr, the circular path of radius ‘r’, then its velocity ‘v’ is given by v , ., t, , www.topperlearning.com, , 8