Given:

A runner travels around rectangle track.

length of track= 50 meters

width of track = 20 meters

runner travels around the rectangle track two times  and finally finishes back at the starting point.

To Find:

Distance and displacement of runner.

Solution:

Distance traveled by runner = 2 (perimeter of rectangle)

Perimeter of rectangle = 2(L+B)

L = 50 m     B = 20 m

perimeter of rectangle = 2(50+20)

                                       = 140 m

Distance traveled by runner = 2 (perimeter of rectangle)

                                                = 280 m

Displacement :

It is the shortest distance between initial and final position or the shortest path of travel

initial position of runner = final position of runner

displacement = 0 m

Distance traveled by runner = 280 m

Displacement traveled by runner = 0 m

Euclid was an ancient Greek mathematician who lived in the Greek city of Alexandria in Egypt 

Euclid is often referred to as the 'father of geometry' and his book <i>Elements</i> was used well into the 20th century as the standard textbook for teaching geometry.

The basic processes of life include organization, metabolism, responsiveness, movements, and reproduction. In humans, who represent the most complex form of life, there are additional requirements such as growth, differentiation, respiration, digestion, and excretion. All of these processes are interrelated.

The human body consists of a bony skeleton and muscles. The three main parts of the body are: the head, the trunk and the limbs (extremities). The head is composed of the cranial and facial parts. It contains the brain, the centre of the nervous system.

Plasma is a state of matter that is often thought of as a subset of gases, but the two states behave very differently. But unlike ordinary gases, plasmas are made up of atoms in which some or all of the electrons have been stripped away and positively charged nuclei, called ions, roam freely. Plasma is considered as the fourth state of matter. Plasma is similar to the gas. Particles of plasma are made of free electrons and ions.

• Velocity – Time Graphs:

The variation in velocity with time for an object moving in a straight line can be represented by a velocity-time graph. In this graph, time is represented along the x-axis and the velocity is represented along the y-axis. If the object moves at uniform velocity, the height of its velocity-time graph will not change with time. It will be a straight line parallel to the x-axis. To determine the distance moved by the car from its velocity-time graph, the area under the velocity-time graph gives the distance (magnitude of displacement) moved by the car in a given interval of time.

Matter can be classified as solid, liquid and gas on the basis of inter-molecular forces and the arrangement of particles. These three forms of matter can be converted from one state of matter to another state by increasing or decreasing pressure and temperature. For example, Ice can be converted from solid-state to a liquid state by increasing the temperature.

• States of Matter:

On the basis of physical states, all the matter can be classified into three groups – solids, liquids and gases. Examples of solids, liquids and gases are:

1. Sugar, sand, iron, wood, rocks, minerals and ice are the examples of solids.
2. Water, milk, oil, kerosene, petrol and alcohol are liquids.
3. Air, oxygen, hydrogen, carbon dioxide and steam are gases.

• The Solid State:

Properties of solids:

1. Solids have a fixed shape and a fixed volume.
2. Solids cannot be compressed much.
3. Solids have high densities. They are heavy.
4. Solids do not fill their container completely.
5. Solids do not flow.

• The Liquid State:

Properties of liquids:

1. Liquids have a fixed volume but they have no fixed shape.
2. Like solids, liquids cannot be compressed much.
3. Liquids have moderate to high densities. They are usually less dense than solids.
4. They do not fill their container completely.
5. They generally flow easily.

• The Gaseous State:

Properties of gases:

1. Gases have neither a fixed shape nor a fixed volume.
2. They can be compressed easily.
3. They have low densities.
4. They fill their container completely.
5. They flow easily.

Lysosomes

• The sac-like structures in a cell surrounded by membrane are called lysosomes.
• They keep the cells clean by digesting and breaking the outside materials like bacteria, food entering the cell or worn-out cell organelles into small pieces.
• They can digest these organic materials due to the presence of strong digestive enzymes that can brreak down organic compounds. Therefore, lysosome is also known as a suicide sac.
• Many scientists believe that lysosomes are not present in plant cells and their function of lysosomes in plants is performed by vacuole.

Lysosomes are membrane-bound sacs filled with digestive enzymes. They are a kind of waste disposal system of the cell. They help to keep the cell clean by digesting any foreign material as well as worn-out cell organelles. Foreign materials entering the cell, such as bacteria or food, as well as old organelles end up in the lysosomes, which break them up into small pieces because they contain powerful digestive enzymes capable of breaking down all organic material. If their covering membrane breaks as it happens during injury to cell, the digestive enzymes will spill over the cell contents and digest the same. As lysosomes are organelles which on bursting can kill cells possessing them, they are called suicide bags.

Plasma membrane called a selectively permeable membrane because it regulates the movement of substances from within to outside of the cell. This means that the plasma membrane allows the entry of some substances while preventing the movement of some other substance.

It is given that the ratio of hydrogen and oxygen by mass to form water is 1:8. Then, the mass of oxygen gas required to react completely with 1 g of hydrogen gas is 8 g. Therefore, the mass of oxygen gas required to react completely with 3 g of hydrogen gas is 8 — 3 g = 24 g.

Sponge is compressible because it is having minute pores in which air is trapped .on presssing the air is expelled. it is still considered as a solid because it has a definite volume and shape does not changes unless compressed.

Molecules -

1. Molecules refers to combinations for more than 1 atom.

2. A molecule is molecular level and have its chemical properties.

3. It is at the chemical level that represents chemical properties of that element through out the reaction.

Particles -

1. Particles are not clear word in their sense. Particles refer to any assumed small thing that exist

2. It is not necessary that a particle have its own chemical properties.

3. It is not chemical level of organisation. It can be notices with nacked eyes or using simple microscope.

Acceleration of a body is defined as the rate of change of its velocity with time. 

Acceleration = change in velocity/time taken

If the velocity of an object changes from an initial value u to the final value v in time t, the acceleration a = v–u/t. The acceleration is taken to be positive if it is in the direction of velocity and negative when it is opposite to the direction of velocity. The SI unit of acceleration is ms^–2.

If an object travels in a straight line and its velocity increases or decreases by equal amounts in equal intervals of time, then the acceleration of the object is said to be uniform. The motion of a freely falling body is an example of uniformly accelerated motion. On the other hand, an object can travel with non-uniform acceleration if its velocity changes at a non-uniform rate. For example, if a car travelling along a straight road increases its speed by unequal amounts in equal intervals of time, then the car is said to be moving with non-uniform acceleration.

 Initial Speed  (u)= 54 km /hr = 54 *1000 m / 3600 s = 54*5/18 = 15 m/s
         ( 1km = 1000 m and 1hr = 60 mins = 60*60 seconds = 3600 seconds)
        Time = 8 seconds
       Final Velocity (V) = 0
 we know that ,
         v = u + at
         0 = 15 + a*8
       0 = 15 + 8a
       a= -15/8 m/s²
   Therefore , acceleration is -15/8 m/s²
also ,
           S = ut+1/2at²
           S = 15*8² + 1/2 *(-15/8)*8²
              =15*64 - 15*4
             = 15(64 - 4)
             =15(60)
             S=900 m
hence Stopping Distance traveled before stopping is 900m .

A car travels along the straight road 100 m east, then 50 m west. The total distance covered by the car is equal to the total path covered by it. In this case, distance of the car is equal to 100 m + 50 m = 150 meters.

The shortest path covered by the car is called its displacement. It is given by :

{tex}d=\sqrt{100^2+50^2} \\\\d=111.8\ m{/tex}

Hence, the distance and displacement of the car is 150 m and 111.8 m respectively.

A balloon shrinks inside a fridge because of the way gases behave. If the pressures remain the same on a fixed mass of gas, a drop in temperature will reduce the volume of the gas. The gas molecules get closer together and the density increases.