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Topic 2: KinematicsGraphical Analvsis of motion

Gradient

of displacement-time graph

Displacement

Area under eraph

of velocity -time graph

Acceleration

Equations of uniformlv accelerated motionThe 4 kinematics equations can only be used when the acceleration of the motion is constant.ln I9Stj!9!L!1qI]S! (straight line motion), the 4 kinematics equations can be applied directly.

o{ acceleration time grdph

r=1(,,+,,tt tt':tt2-2aspositive direction.a negative sign.

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Note: Usually, the direction of the initial velocity is taken as theVector (v, s or a) which has an opposite direction is givenDisplacement is always measured from its initial positionProiectile Motionln non-linear motion (2D projectile motion), we have to consider the r lhoizontall and J(rerlical) components of u, v, s and a separately. Time t is a scalar - it is the gdllqla4ilflllq!links the )r motion to the y motion.

ofvelocity-time graph

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(

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Tvpical approach to solvine such questionsStep 1: Sketch the tra,ectory including labeling all the quantities {very important!)Step 2: Resolve the initial velocity, ll (if necessary)Step 3: List down the quantities given by the question:

Step 4: Apply the kinematics equations- Remember that time links the horizontal motion to- the vertical motionAil resistanceAir resis6nce is a resistive force that opposes the motion of an object as it tries to push air(fluid) particles out ofthe way. lt depends on the shape and speed ofthe object.Direction of air resistance: opposite to the direction of motionMagnitude of air resistance: increases with speed ofthe objectConsider an obiect being proiected verticallv u'pwards:

While it is moving upwards, air resistance acts in the same direction as its weight.

weight- The object will decelerate at a higher rate than g.

As the object travels higher, its speed will decrease. The air resistance will alsodecrease until zero,- Maximum height reached by the obiect wall be lower than that without alr resistance.At this point, air aesistance is zero.

Considering horizontal motion I Considerins verttcal motion (take note of signrrr = ,r (th is is true for free-falling obj ect) I conventions I| /, =? {rhis is zero if initiat motion of object isr, I horizontdl)a,: 0 (this is zero for free-falling object) | .t, = ? {this is zero if object returns to originalI position / same level as original position)I r,y - ? (this is zero atthe max height of the

traiectory)dr, : g {this is gravitational acceleration forfree-falling obiect)

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Consider an obiect movi rachutistl:

Jair".tion ot rotion

time

path without air resistance

rds {this is like the tvDical moti n of a fallilnitially speed of object is zero and acceleration is g.As the object gains speed. air resistance is no longer zero. lt acts in the directionopposite to its weight-

resistatIweightlhe oble( t will a( celerdte slower thdn g.As the object falls further, its speed will increase- The air resistance will also increaseuntil its magnitude equals its weight.The resultant force on the object is now zero. The speed of the object remainsconstant thereafter -the terminal velocitv (Vr).

velocity

For 2D projectile motion under ot resistohce. the projeciion will:(d) rcoch lowetthdn its maximum possibte height;(b) redch thortet thon its maximum possible range;H take shortertime to reoch its top thon its woy down;(d) hdve on dsymmetficdl path.

3lPase

path with air resistance '..

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Practice

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