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Rest And Motion | Speed Notes
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Rest And Motion
Motion: An object is said to be in motion when its position changes with respect to the reference point 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.
Reference Point:
A specific point with respect to which we describe the location of an object is called a reference point.
A body can be at rest as well as in motion at the same time with respect to two different reference points.
Therefore, Rest and Motion are relative terms not absolute terms.
Rest and Motion are relative tems. Since a body may be at rest relative to one object and simultaneously it may be in motion relative to another object.
Example: a passenger sitting in a moving vehicle is at rest with respect to his fellow passenger but he is in motion with respect to a place outside the bus.
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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. |
Speed And Velocity
Speed:
- Speed or Average 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.
- For non-uniform motion, the average speed of an object is obtained by dividing the total distance travelled by an object with the total time taken.
- Instantaneous Speed:
- Speed of a body at an instant, that is at a very short span is known as Instantaneous Speed.
- For a uniform motion, the average speed of an object is equal to its instantaneous speed throughout the path.
Velocity
Velocity Or Average Velocity:
- In case of a uniform motion in a straight path, the average velocity is equal to its instantaneous velocity throughout its path.
- Velocity (average 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 distance covered by a body per unit time. In other words, it is the rate of change of distance. | It is defined as the Net Displacement of a body per unit time In other words, it 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. |
Velocity is directed speed. | |
Speed may or may not be equal to velocity. | A body may possess different velocities at different positions, but the same speed. |
For a moving body speed never decreases with time for a moving body. | For a moving body velocity can decrease or increase. |
In case of a moving body, speed never become zero. | In case of a moving body, Velocity can be zero. |
Speed in SI is measured in ms^{-1} | Velocity in SI, is measured in ms^{-1} |
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 at^{2}
(ii) The equation for position-time relation:
Derivation of v^{2} – u^{2} = 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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