Distance : Every day we walk and use to travel distance like we visit market, friends home, office,playground, school,college and many more places without physical movement of our body we can’t travel any distance and similarly for any vehicle motor car can’t travel any distance without energy,engine and it should be not disorder then distance can be travel. below some picture for reference.
Displacement: this is define as join the straight line from initial position to final position no need to see the path only join initial and final position through straight line this will give displacement hence displacement is difference between final and initial position. now every quantity has its own characteristics like human every one has name and some identity to recognize him like engineer, doctor, teacher, police and many more in similar way every quantity has identity and this is categorizes in two part one is called vector and other is called scalar one more category tensor but in our study only two is important so we will see now this two category one by one.
Vector: this is actually part of math then question arises why we study in physics ? the answer is for physicist math is like a soldier gun infect math is tool of physics if you want to learn physics then you should have good knowledge of math in lower classes you have studies physics and you have used math like you have study about light incidence on a surface and reflect back here you have seen angle of reflection, angle of incidence and line what is this we study about angle and line in mathematics but we study light in physics so math is important for physics i hope you have understand what i want to say and why we need to study vector here because important to learn physics.
now direction of physical quantities suppose on a door written as pull and a man came and pushing the door with large force try to open door to inter in the room tell me will door open of course no because he is applying force in wrong direction force is a physical quantity hence for physical quantity direction is important but not for all physical quantities only for vector quantity now which is vector quantities answer is those quantities which has magnitude as well as direction both is important for a vector quantities magnitude fixed the quantity and direction specify the quantity, fixed means how much and specify means whether it has direction or not so a physical quantity is vector quantity if and only if it has magnitude and direction both example 10 newton force towards left or right so force is a physical quantity which has direction and is called vector quantity, take another physical quantity velocity is direction important for velocity of course yes if direction is not associated with velocity you will not reach at your destination suppose you want to go to your friend home his house is located in east direction 1000 m from your home and you start to move in west direction with constant speed of 2 m/s hence after 500 s you will travel distance 1000 m but you will not reach your friend home because you have chosen wrong direction west but your friend home is located in east. hence velocity is vector quantity, take another example temperature suppose we are at very cold place where temperature is -20 C⁰ here direction is important big no because in all direction temperature will be same we can’t say east temperature is -20 C⁰ awkward here only magnitude is important for temperature and hence it is a scalar quantity, take an another physical quantity mass suppose in a sack 50 kg of rice is packed here direction is important big no because we can say 50 kg rice is in left, right, up and down direction awkward hence it is also a scalar quantity no direction associated with mass only magnitude 50 kg rice. now what is advantage of vector ? suppose i am standing in a ground field and you are also with me i told you hey Jack one bag of gold is 100 m from here suppose you are not seeing that bag brought it quickly then how you will brought that bag in minimum time if you are intelligent you will run away 100 m from our position and round a circle of 100 m radius you will found gold bag somewhere and you will brought to me and it takes 5 minute time oh no maximum time now suppose i given you direction gold bag is 100 m 30⁰ east then you will point to directly at gold bag no circle round up required exact position of gold bag is known hence you will brought it in 1 minute i will be happy oh good so in similar fashion computer work to fetch data from memory in second using vector magnetic field now i hope your vector and scalar quantity identity is clear we will study vector in more details in vector topic latter only here overview to recognize quantity distance and displacement hence distance is scalar quantity no direction associated with distance but displacement is a vector quantity direction must associated with displacement. now we will see some similarity in distance and displacement given below.
|1 is basically length unit m
||1 is basically length unit m
|2 Length of path travelled actually
||2 Straight line difference between two position
|3 it is a scalar quantity
||3 it is a vector quantity
|4 Distance is always larger than displacement
||4 Displacement is smaller than distance
|5 Minimum value of distance is equal to magnitude of displacement
||5 in straight line travel magnitude of distance and displacement are same
|6 Between two points there may be many value of distance
||6 Between two points displacement has a unique value
Now with distance another quantity is involve that is time when we travel distance how much time taken to travel certain distance combining these two quantity distance and time we made a new physical quantity that is speed then what is speed ?
Speed : this is define as the distance travel in one second by any particle or object is called speed of that particle or object hence speed is basically distance travel per unit time so condition is per unit time so it gives speed now if distance d is travelled in t second then speed V = d/t or speed = distance/time mathematical formula now its dimension is
|V| = M᠐L¹T⁻¹ = L¹T⁻¹ or its unit is m/s in si system now tell me speed is scalar quantity or vector quantity answer is scalar quantity why ? because see the formula of speed = distance/time we know that distance is scalar and time is also scalar hence combination of two scalar quantity gives a scalar quantity hence speed is scalar quantity now we made some classification of speed.
Classification of speed :
Uniform speed we made definition of speed distance/time that is distance per second but in practical we don’t take one second to travel distance we take many second to travel distance like 50 second 5 minute, 2 hour and so on depending upon distance but suppose we want to travel 500 m distance in 10 second then our speed will be 500/10 = 50 m/s here total time is 10 second so in first second we will travel 50 m in second second 50 m in third second 50 m hence in every second our distance travel is same this type of speed is called uniform speed means speed is constant in every second hence equal distance travel in equal interval of time is uniform speed.
Non-uniform Speed this is define as unequal distance is travelled in equal interval of time is called non-uniform speed means to say that in first 3 second travel 6 m in second interval 3 second travel 10 m in third interval 3 second 15 m or in fourth interval 3 second travel 3 m so unequal distance travelled in equal interval of time hence this is called non-uniform speed understand interval time will be same now next is instantaneous and average speed.
instantaneous and average speed: To understand this speed we take an example i want to travel a distance of 40 km by bike and how i travel this distance is given below.
d = 10 km d= 5 km d= 0 km d= 25 km
A→→→→B→→→→C→→→→→→D→→→→→→→E time t=5′ t= 10′ t=5′ t= 20′
here total distance A to E is 40 km.
in A to B travelled distance 10 km in 5 minute so speed V₁= 10/5 = 2 km/minute.
in B to C travelled distance 5 km in 10 minute so speed V₂= 5/10 = 0.5 km/minute
in C to D distance travelled 0 km in 5 minute so speed V₃= 0/5 =0 since here taking rest for tea.
in D to E distance travelled 25 km in 20 minute so speed V₄= 25/20 =1.25 km/minute now see here speed V₁, V₂, V₃, V₄ instantaneous speed so speedometer gives instantaneous speed of bike at a particular moment or instant of time hence instantaneous speed = (distance travelled in given time)/very small time period at that instant this can be written as instantaneous speed = ∆d/∆t where ∆t is very small as much ∆t will be small average speed value will be accurate but question is how much small value we can write answer is not possible to write you can think 10 cm of length by all person of this world how small it will be just imagine now at this point simple math was failed and Mr Newton stuck here for three years then he invented calculus to write such small value hence we take here help of calculus and write as ∆d/∆t where ∆t→0 not zero but approaching to zero hence our equation now became ds/dt = average speed = V
here total distance is 40 km and total time taken to travelled is 40 minute hence average speed V = 40/40 = 1 km/minute this is called average speed hence average speed = total distance/total time now we will see velocity.
Velocity: this is define as displacement per unit time that is V = displacement/time its dimension will be same as speed unit is also same m/s in si system now displacement is a vector quantity hence velocity is a vector quantity direction associated with velocity now all about velocity we will study in next post thanks for reading.
Distance and displacement easy concept
dated 22nd April 2018.