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Mensuration | Assess
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Mensuration | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Perimeter: Length of boundary of a simple closed figure. Perimeter of Rectangle = 2(l +b)Perimeter of Square = 4aPerimeter of Parallelogram = 2(sum of two adjacent sides)Area: The measure of region enclosed in a simple closed figure. Area of a trapezium = half of the sum… readmore
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Perimeter: Length of boundary of a simple closed figure.
Perimeter of Rectangle = 2(l +b)
Perimeter of Square = 4a
Perimeter of Parallelogram = 2(sum of two adjacent sides)
Area: The measure of region enclosed in a simple closed figure.Area of a trapezium = half of the sum of the lengths of parallel sides × perpendiculardistance between them.
Area of a rhombus = half the product of its diagonals. (Scroll down till end of the page)
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Mind Map Overal Idea Content Speed Notes Quick Coverage Rest And Motion The terms Rest and Motion are relative. Motion: An object is said to be in motion when its position changes with time. Rest: An object is said to be at rest when its position does not change with respect to a reference point… readmore
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Rest And Motion
The terms Rest and Motion are relative.
Motion: An object is said to be in motion when its position changes with time.
Rest: An object is said to be at rest when its position does not change with respect to a reference point with time.
A specific point with respect to which we describe the location of an object is called a reference point. (Scroll down till end of the page)
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Distance and Displacement
- Distance: The total length of path covered by an object is said to be the distance travelled by it.
- Displacement: Gap between the initial and final positions of an object is said to be its displacement. Or
- The length of a line segment that joins the initial and final positions of an object is known as the displacement.
Difference Between Displacement and Displacement
Distance Displacement Distance is defined as the total length of the path travelled by an object to go from one point to another. Displacement is defined as the length of the line segment that joins the initial and final positions of an object. Since distance has only magnitude and its direction cannot be specified always, it is a scalar quantity. Since displacement has magnitude and it is specified in a direction from initial position to final position, it is a vector quantity. Distance can only have positive values. Displacement can have both positive and negative values. Distance depends on the length of the path travelled. Displacement depends only on the initial and final point regardless of the path travelled. Difference Between Displacement and Displacement Speed And Velocity Speed
- Speed: The distance travelled by an object in unit time is referred to as speed.
- Its S.I unit is m/s.
- In general speed refers to average speed.
- Average speed: For non-uniform motion, the average speed of an object is obtained by dividing the total distance travelled by an object by the total time taken.
- For a uniform motion, the average speed of an object is equal to its instantaneous speed throughout the path.
Velocity
- Average Velocity or Velocity : For a uniform motion in a straight path, the average velocity is equal to its instantaneous velocity throughout the path.
- Velocity of an object is equal to the instantaneous velocity of an object.
Differences Between Speed and Velocity
SPEED VELOCITY It is defined as the rate of change of distance. It is defined as the rate of change of net displacement. It is a scalar quantity. It is a vector quantity. It can never be negative or zero. It can be negative,zero or positive. Speed is velocity without direction. Velocity is directed speed. Speed may or may not be equal to velocity. A body may possess different velocities but the same speed. Speed never decreases with time. For a moving body, Velocity can decrease with time. For a moving body , it can be zero. Speed is never zero. Velocity can be zero. Speed in SI is measured in ms-1 Velocity in SI, is measured in ms-1 Differences Between Speed and Velocity Uniform And Non-Uniform motion
- Uniform motion or non accelerated motion: When an object covers equal distances in equal intervals of time, it is said to be in uniform motion. Uniform motion is a non-accelerated motion.
- Non-uniform motion or accelerated motion: Motions where objects cover unequal distances in equal intervals of time. Uniform motion is an accelerated motion.
Acceleration
Acceleration: Change in the velocity of an object per unit time.
Graphical representation of motions
(i) Distance-time graph
For a distance-time graph, time is taken on x-axis and distance is taken on the y-axis.
[Note: All independent quantities are taken along the x-axis and dependent quantities are taken along the y-axis.]
(ii) Velocity-time graph
Equation of motion by graphical methods
Derivation Of Equations Of Motion
Equations of motion can be derived by two methods. They are (i) Graphical Method. (ii) Algebraic Method
Derivation of The Equations of Motion By Algebraic Method:
(a) Velocity-time relation:
Derivation of S = ut + ½ at2
(ii) The equation for position-time relation:
Derivation of v2 – u2 = 2as
(iii) Equation for position-velocity relation:
Conclusions From a Distance – Time Graph
Uniform Circular Motion
When a body moves in a circular path with uniform speed, its motion is called uniform circular motion.
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Motion and Time | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Motion: The action or process of moving or being moved. The distance moved by an object in a unit time is called its speed. Speed of objects help us to decide which one is moving faster than the other. The speed of an object is the… readmore
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Motion: The action or process of moving or being moved.
The distance moved by an object in a unit time is called its speed.
Speed of objects help us to decide which one is moving faster than the other.
The speed of an object is the distance travelled divided by the time taken to cover that distance.
Its basic unit is mere per second (m/s). (Scroll down till end of the page)
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Periodic events are used for the measurement of time.
Periodic motion of a pendulum has been used to make clocks and watches.
Motion of objects can be presented in pictorial form by their distance-time graphs.
The distance-time graph for the motion of an object moving with a constant speed is a straight line.
Uniform Motion ANd Non – Uniform Motion:
- Uniform motion: An object moving with a constant speed is said to be in uniform motion. The average speed is the same as the actual speed.
- Non-Uniform motion: If the speed of a moving object keeps changing, the object is said to be in non-uniform motion.
Speed: It is the distance covered by an object in a unit time.
Speed = Total distance/ Total Time
Basic unit of speed is m/s.
Distance-Time Graph: Motion of objects can be presented in pictorial form by their distance-time graphs.
The distance-time graph for the motion of an object moving with a constant speed is a straight line.
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Perimeter and Area | Assess
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Perimeter and Area | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Perimeter is the distance around a closed figure whereasarea is the part of plane occupied by the closedfigure. Area is the measure of the part of plane or regionenclosed by it. (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content We… readmore
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Perimeter is the distance around a closed figure whereasarea is the part of plane occupied by the closedfigure.
Area is the measure of the part of plane or regionenclosed by it. (Scroll down till end of the page)
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We have learnt how to find perimeter and area of a squareand rectangle earlierclass.
They are:
(a) Perimeter of a square = 4 × side
(b) Perimeter of a rectangle = 2 × (length + breadth)
(c) Area of a square = side × side
(d) Area of a rectangle = length × breadth Areaof a parallelogram = base × height
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