CBSE - Grade 9 - Physics - Ch 1 - Motion (PDF Format)
CBSE Class 9 β Science (Physics) β Chapter 1: Motion β Summary Notes πΉ Motion An object is said to be in motion if its position changes with time with respect to a fixed point. πΉ Types of Motion Uniform Motion: Equal distances in equal time intervals. Non-uniform Motion: Unequal distances in equal time intervals. πΉ Distance vs Displacement Distance: Total path length, scalar quantity. Displacement: Shortest distance from initial to final position, vector quantity. πΉ Speed and Velocity Speed = Distance / Time (scalar) Velocity = Displacement / Time (vector) Uniform Speed/Velocity: Constant speed/velocity. Non-uniform Speed/Velocity: Changing speed/velocity. Average Speed = Total Distance / Total Time Average Velocity = Total Displacement / Total Time πΉ Acceleration (a) Rate of change of velocity. π = π£ β π’ π‘ a= t vβu β where π’ u = initial velocity, π£ v = final velocity, π‘ t = time Positive acceleration = speeding up Negative acceleration (retardation) = slowing down πΉ Equations of Uniformly Accelerated Motion π£ = π’ + π π‘ v=u+at π = π’ π‘ + 1 2 π π‘ 2 s=ut+ 2 1 β at 2 π£ 2 = π’ 2 + 2 π π v 2 =u 2 +2as (Where π s is displacement) πΉ Graphical Representation Distance-Time Graph: Straight line = uniform speed Curved line = non-uniform speed Velocity-Time Graph: Straight line (positive slope) = uniform acceleration Area under v-t graph = displacement πΉ Uniform Circular Motion Motion in a circle at constant speed Velocity direction keeps changing, hence acceleration is present It is accelerated motion even with constant speed πΉ Key Formulae Recap Speed = Distance / Time Velocity = Displacement / Time Acceleration = (Final velocity β Initial velocity) / Time π£ = π’ + π π‘ v=u+at π = π’ π‘ + 1 2 π π‘ 2 s=ut+ 2 1 β at 2 π£ 2 = π’ 2 + 2 π π v 2 =u 2 +2as
CBSE - Grade 9 - Physics - Ch 1 - Motion (PDF Format)
- 2. MOTION PHYSICS Rest and Motion Motion ο· 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. ο· 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. ο· To locate the position of an object, we have to choose some suitable reference point called the origin. Distance and Displacement ο· The distance travelled by an object is the length of the actual path traversed by the object during motion. It is a scalar quantity. ο· 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. ο· The distance travelled by an object in motion can never be zero or negative. ο· The displacement of an object can be positive, zero or negative. Never can the distance travelled be less than the displacement. ο· Both distance and displacement have the same units.
- 3. MOTION PHYSICS Uniform motion Motion Non-uniform motion Uniform and Non-uniform Motion ο· 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. ο· An object is said to have non-uniform motion if it travels unequal distances in equal intervals oftime. Speed ο· 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). Speed ο· If βsβ is the distance travelled by a body in time βtβ, then its speed βvβ is given as v ο· Speed of a body is a scalar quantity. It can be zero or positive but can never benegative. ο· 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). ο· 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). ο· For bodies moving with non-uniform speed, we describe the rate of motion in terms of their average speed. Average speed= Total distance travelled Total time taken Distancetravelled Time taken s t
- 4. MOTION PHYSICS vav Velocity ο· Velocity of a body is defined as the distance travelled by the body in unit time in a givendirection. ο· The SI unit of velocity is the same as that of speed, i.e. metre/second (m/s). Velocity or, Velocity i.e. where v is velocity and s is displacement of the body in time t. ο· Velocity of a body is a vector quantity. It can be positive, negative or zero. ο· 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 maybe. ο· 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. ο· 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 Initial velocity + Final velocity 2 or vav u v 2 where βuβ is initial velocity, βvβ is final velocity and is average velocity. Distance travelled in a given direction Time taken Displacement Time taken v s t
- 5. MOTION PHYSICS Acceleration ο· 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 where βuβ is initial velocity, βvβ is final velocity, βaβ is acceleration of the body and βtβ is time taken for change in velocity. ο· Acceleration is a vector quantity. It can be positive, negative or zero. The SI unit of acceleration is metre per second square (m/s2 ). ο· 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. ο· 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. ο· 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. ο· A body is said to possess non-uniform acceleration if its velocity changes by unequal amounts in equal intervals of time. DistanceβTime Graph ο· The distanceβtime graph of a body moving with uniform speed is a straight line. ο· Speed of a body can be obtained from the slope of the distanceβtime graph. v - u t
- 6. MOTION PHYSICS ο· Let s1 and s2 be the distance travelled by the object in time t1 and t2, respectively. Here (s2 β s1) gives the distance travelled by the body in time interval (t2 β t1). Speed v ο· The distanceβtime graph of a body moving with non-uniform speed is a curved line with a variable slope indicating variable speed. VelocityβTime Graph ο· The velocityβtime graph of a body moving with uniform velocity is a straight line parallel to the time axis. ο· The magnitude of displacement or distance travelled by the body is equal to the area enclosed by the velocityβtime graph and time axis. Distance travelled = Speed Γ Time taken = OA Γ OC = Area of rectangle OABC Distancetravelled Time taken s2 s1 t2 t1
- 7. MOTION PHYSICS ο· The velocityβtime graph of a body moving with uniform acceleration is a straight line inclined to the time axis. o The slope of the velocityβtime graph represents the acceleration of the body. Acceleration o The area enclosed by the velocityβtime graph and time axis gives the distance travelled by the body. Distance travelled = Area of ABCDE = Area of triangle ADE+ Area of rectangle ABCD = ο· The velocityβtime graph of a body moving with non-uniform acceleration can have any shape, indicating variable speed. Change in speed ED Time taken AD 1 AD DE + AB BC 2
- 8. MOTION PHYSICS v = u + at s = ut + (1/2) at2 v2 - u2 = 2as Equations of Motion ο· The three equations of motion of a body moving along a straight line with uniform acceleration are where βuβ is initial velocity of the body which moves with uniform acceleration βaβ for time t, βvβ is final velocity and βsβ is distance travelled by the body in time t. Uniform Circular Motion ο· When a body moves along a circular path with a uniform speed, its motion is called uniform circular motion. ο· Examples: Motion of the Moon around the Earth, a cyclist moving in a circular track at constant speed ο· 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. ο· The external force needed to make a body travel in a circular path is known as centripetal force. ο· The circumference of a circle of radius βrβ is given by 2ο°r. If a body takes βtβ seconds to go once round the circular path of radius βrβ, then its velocity βvβ is given by v ο½ 2Οr . t