Physics – Classical Mechanics - Quick Guides | Physics

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Study GuidePhysics–Classical Mechanics1.Kinematics in One DimensionKinematics is the branch of physics that studieshow objects move, without worrying aboutwhytheymove. In this chapter, we focus on motion along a straight line and explore the relationships between:•Displacement (d)•Velocity (v)•Acceleration (a)•Time (t)Among these,displacement, velocity, and acceleration are vector quantities, which means theyinclude both size and direction.1.Vectors and ScalarsWhat is a Vector?Avectoris a physical quantity that has:•Magnitude(how much), and•Direction(which way)Examples of vectors:•Velocity•Displacement•ForceVectors are often shown usingarrows. Thelengthof the arrow represents magnitude, and thearrowheadshows direction.

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Study GuideWhat is a Scalar?Ascalarhas only magnitude andno direction.Examples of scalars:•Time•Temperature•Distance1.Displacement and VelocityImagine a car starting from a signpost on a road. To describe where the car is later, we must know:•How far it moved, and•In which direction it moved2.DisplacementDisplacementis thechange in positionof an object.It is a vector, so it includes direction.Example:•10 km east•−5 m (meaning 5 m in the opposite direction)Displacement is not the same as distance traveled.If a car travels:•1 km east, then•1 km west back to its starting pointThetotaldisplacement is zero, even though the car traveled 2 km.

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Study Guide3.Average VelocityVelocitydescribes how fast an object movesand in which direction.Theaverage velocityis defined as:Units: meters per second (m/s)4.Average AccelerationAccelerationtells us how quickly velocity changes over time.It is calculated using:Units:•m/s² (meters per second squared)Acceleration can be:•Positive(speeding up in the positive direction)•Negative(slowing down or speeding up in the opposite direction)2.Graphs in KinematicsGraphs help us visualize motion and understand relationships between displacement, velocity, andacceleration.1.Distance–Time GraphAdistance–time graphshows how far an object moves as time passes.•Ahorizontal line→ object is at rest

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Study Guide•Astraight sloping line→ constant velocity•Asteeper slope→ higher speedTheslope of the graphgives thespeed.2.Velocity–Time GraphAvelocity–time graphshows how velocity changes with time.•Theslopeof this graph givesacceleration•Thearea under the graphgivesdisplacementFor example:•A triangular area represents increasing or decreasing velocity•A rectangular area represents constant velocity

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Study Guide3.Instantaneous Velocity and Acceleration1.Instantaneous VelocityThis is thevelocity at a specific moment in time—like what a car’s speedometer shows.On a graph:•It is found by drawing atangentto the distance–time curve•Theslope of the tangentgives the instantaneous velocity2.Instantaneous AccelerationInstantaneous acceleration is found in a similar way:•Draw atangentto the velocity–time graph•Theslope of that tangentgives acceleration at that moment3.Connecting the Three GraphsWhen distance–time, velocity–time, and acceleration–time graphs are placed one above the other:

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Study Guide•You can finddisplacement, velocity, and acceleration at the same instant•This makesanalyzing motion much easier5.Negative Acceleration (Deceleration)Negative acceleration doesnot always mean slowing down.It can happen in two cases:•Case 1:Velocity is positive, but decreasing•Case 2:Velocity is negative, but increasing in magnitudeExample:A ball thrown upward:•Slows down while moving upward

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Study Guide•Stops momentarily at the highest point•Speeds up downward due to gravity6.Motion with Constant AccelerationWhen acceleration is constant:•Velocity changes at a steady rate•Average acceleration equals instantaneous accelerationUsing:•Initial velocity (v₀)•Final velocity (vᶠ)•Acceleration (a)•Time (t)•Displacement (d)We can describe motion using four key equations.7.Kinematic Equations (One Dimension)1.vᶠ=v₀+ atVelocity as a function of time2.d = ½ (v₀+ vᶠ)tDisplacement using average velocity3.d = v₀t + ½at²Displacement as a function of time

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Study Guide4.vᶠ² = v₀² + 2adVelocity as a function of displacementEach equation usesfour of the five variables, allowing you to solve problems efficiently.2. Kinematics in Two DimensionsIn real life, motion usually happens in more than one direction. To make problems easier tounderstand, we often describe motion usingtwo dimensions, usually thex-direction (horizontal)andy-direction (vertical).Examples of two-dimensional motion include:•A ball thrown into the air•A projectile moving across the ground

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Study Guide•An object moving in a circular pathTo study this kind of motion, we usevectorsand basic vector algebra.1.Vector Addition and Subtraction: Geometric MethodVectors can be moved anywhere on a pageas long as their length and direction stay the same.This allows us to add and subtract them graphically.1.Adding Two VectorsSuppose:•Vector Arepresents a velocity of 10 m/s toward the northeast•Vector Brepresents a velocity of 20 m/s at 30° north of eastTo add vectors graphically:1.Place thetail of one vector at the head of the other2.Theresultant vector(C)goes from the tail of the first vector to the head of the secondThelengthof the resultant gives its magnitude, and theangleit makes with the horizontal gives itsdirection.

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Study GuideOrder of Addition Does Not MatterVector addition follows thecommutative property:•A + B = B + AWhen vectors are placed tail-to-tail, the resultant is thediagonal of a parallelogramformed by thetwo vectors.Adding Several VectorsWhen adding more than two vectors:•Place themhead-to-tail, one after another•The resultant is the vector that closes the polygon2.Subtracting VectorsTo subtract vectors:•Place theirtails together

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