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.
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.
Kinematics in One Dimension motion example
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 .