Meaning of motion if any body or particle is moving then it is called that body or particle is in motion, like if you are walking then you are in motion if you are sitting at position then you are not in motion you will find motion example in the world everywhere so motion is very important take some example of motion to understand concept, Moon is moving around the Earth so moon is in motion, Earth is rotating about its axis so Earth is in motion, Air is blowing so air is in motion,in Sea water is in motion, Aeroplane is moving ,train is in motion,watch needle in motion, in room fan is in motion so everywhere is motion, infect where you are not seeing motion, there is also motion like a lady is sitting on a chair you will say there is no motion because she is at rest but think in lady body blood, heart and kidney are in motion lady taking breath air is coming in and out so air is in motion. now in your room wall is at rest you will say there is no motion but think in wall there is many many atoms inside atoms there are many many electrons which are in motion so think how much of electrons are in motion inside the wall so everything in motion big body and small particle all are in motion hence aim of physics is to understand natural world so it is very important to understand motion hence we want to learn motion so “kinematics is a branch of physics in which we study how to describe motion”.
Here we are studying straight line motion its mean that body or particle will move in a straight line only not on a curve path.
Trajectory : Path of an object like electron revolve in an atom in circular path hence trajectory of electron is circular.
Meaning of dimension see below picture for dimension.
|Kinematics one direction motion in physics
Now from above figure 1-D object is a pencil so for one dimension motion only one axis is sufficient to analyse motion for every point on straight line similarly for 2-D motion badminton object or any play ground on earth surface is two 2D here for any point motion two axis is required to describe motion now for 3D object is truck two analyse any point motion we required three axis like whenever any football player running on ground is 2D motion but sometime jump to hit the ball in air now this is 3D motion.
Now for 1D motion object will move in a straight line either along x axis or along y axis but we generally represent 1D motion by x axis see below picture.
f e d a b c
right side taken as positive and left side taken as negative
Variables in kinematics or math in kinematics:
- Instantaneous Velocity
- Average Velocity
- Instantaneous Speed
- Average Speed
Position: Position is a vector quantity, position means “address” if we want to locate someone address then we have to locate district name colony name and house number then we finally reach at that address or position similarly for any body or particle address location we need Cartesian coordinate that is xy plane to locate address or position of a body or particle here we are studying 1D some one plane only x axis is taken.position vector is line joining from origin to given point which position want to determine.
now if we want to write position vector of point a then we can write
Ra = 1i^, for b Rb = 2i^ similarly for for d and e
Rd = -1i^ , Re = -2i^ but this is one dimension motion hence it will be always along x axis so we neglect i^ and written always as
Xa = 1, Xb = 2, Xd = -1, Xe = -2
Displacement : this is define as change in position vector is called displacement, now change word is very very important in physics to understand concept now any quantities change means final minus initial or can write as change = final – initial here it is position vector so “change in position vector” = “final position vector” – “initial position vector” this is displacement it is a vector quantity because position is a vector quantity hence its change will be a always vector quantity now displacement is minimum length vector from final position to initial position joining straight line initial position to final position, vector along shortest path whether body has travel by any path but its shortest path straight line joining initial to final position is only displacement.
Distance: this is define as length of path travel or length of trajectory in which body or particle travel it is scalar quantity
Distance is greater than and equal to displacement
hence distance is path dependent but displacement is only straight line joining initial point to final point and direction from initial to final point.
velocity: this is define as rate of change of position with respect to time and just we have study change of position is displacement hence displacement with time is velocity and this can be written as
→ → → →
V = D/t or (r2 – r1)/t direction of velocity will be same as direction of displacement Concept in general question asked find the velocity of a body at a point.remember to find out velocity minimum two point is required that change in position initial and final point unless there will be no displacement we can’t find velocity. we can’t find velocity at a single point then why question is asked find velocity at a point ? actual meaning of this is define as we take very close to that point two point one left and other right
| ? | hence velocity is define as v= dx/dt hence if ask to you
→ dt ←
find the velocity at a point its meaning that take very close to point a left point and a right point then we calculate like above v = dx/dt otherwise at a single point velocity can’t be find out.
Instantaneous velocity: now it is define as take displacement as much of smallest that is displacement→0 or dx→0 very very small then that velocity will be instantaneous velocity means velocity at a instant or a particular time and written as v = dx/dt
Average velocity: When we take displacement larger distance like two point at far distance picture below point A and B
hence Average velocity is define as = ∆x/∆t this is know as average velocity both are velocity hence both are vector quantity
now for direction average velocity direction is always same as direction of displacement means initial point to final point but for instantaneous velocity its direction is tangent to the asked point towards initial to final point.
Instantaneous Speed : this is define as smallest distance between two point with respect to time, same as instantaneous velocity modulus means scalar quantity and define as |v| = |dx/dt| here in smallest case displacement and distance is same.
Average Speed : this is define as total larger distance path travel with respect to time and define as average speed = distance/t = d/t here in this case displacement and distance are not equal and speed is a scalar quantity.
Acceleration: this is define as rate of change of velocity with respect to time and denoted by a = dv/dt that is change in velocity a = (v2 – v1)/t acceleration is a vector quantity now if velocity and acceleration are in same direction then speed will increase and if velocity and acceleration are in opposite direction then speed will decrease.
Now time for some basic question on this topic.
Q1 A circle having radius R one person travel on circumference from one end to other end and other person travel on radius from one end to other end find the distance travel by both person and their distance ratio.
Ans this is very simple question a⊖b see the circle from question, distance travel by person through circumference = ?R
distance travel by second person on diameter = 2R
now ration = ?R/2R = ?/2 .
Q2 A cube of side having length 4cm a bee is at point A after some time it fly and A to B and B to point D though side length now find the distance travel by bee and also displacement made by bee from A to D
A B Ans here bee fly by side wise and reaches at D hence distance will be = 4+4+4 =12cm
now for displacement recall vector addition for three dimension already study in previous post vector topic displacement is a vector quantity hence will be added by vector rule cube is xyz plane
here AB is along x positive so we can write 4i^ now from B opposite to z direction so -4k^ now in positive y direction so 4j^ hence for final displacement add displacement along all axis
d = 4i^ + 4j^ – 4k^ now for magnitude take modulus
|d| = 4√3
Q3 three velocity of a particle are given below find the type of motion. for each velocity
→ → →
V1 = 2i^ , V2 = 2i^ + 3j^ , V3 = i^ +5j^ – 2k^
Ans very easy V1 is along x direction so it is 1-D motion
V2 is in xy plane so it is 2-D motion
V3 is in xyz plane so it is 3-D motion
your concept is wrong it is not like that all three velocity are straight line V1 is along x axis ok straight line V2 velocity in xy plane but straight line similarly V3 is in xyz plane but straight line then how to recognize 1-D, 2-D, 3-D motion simple when particle is moving in straight line it is 1-D motion, when particle is moving on curve path in a plane like xy,yz,xz then it is 2-D motion, when particle is moving in curve path in two different plane then it is 3-D motion now i hope your concept is clear.
Q4 A boy walks 6m east in 3s and 3m west in 1s find the average speed and average velocity during journey.
Ans first understand question simple.
we know that average speed = total distance/total time
Average speed = (6+3)/(3+1) = 9/4 =2.25m/s
Now for average velocity = total displacement/total time
Average velocity = (6-3)/(3+1) = 3/4 = 0.75m/s
hence it is clear that average speed is greater than equal to average velocity.
Q5 A man goes from point A to B with 60m/s and returned from point B to A with 40m/s find average velocity and average speed.
Ans simple question see below.
from question A to B speed is 60m/s and B to A speed is 40m/s
now average velocity = total displacement/total time here total displacement is zero because finally returned to point A so average velocity = 0m/s
now for average speed = total distance/total time here neither distance nor time is given so let d is distance between point A to B
now speed is given so we can calculate time taken from A to B
T1 = d/60 ( using constant speed formula s= vt similarly time taken from B to A T2 = d/40 hence apply the formula
average speed = total distance/total time = 2d/(d/60+d/40)
average speed = 2*60*40/(60+40) = 48m/s.
Now you can practice yourself more question like this for numerical problems. thanks for reading.
Kinematics one direction motion in physics .