These Class 11 Physics notes for Chapter 3, 'Motion in a Straight Line,' explain fundamental concepts of motion. It defines rest and motion as relative, and categorizes motion into one, two, and three-dimensional based on changing coordinates. The notes differentiate between path length and displacement, highlighting that path length is always greater than or equal to the magnitude of displacement. Key concepts like average speed, instantaneous speed, velocity, and acceleration are defined with their units and dimensional formulas. The text also explains positive and negative acceleration (retardation). Formulas for uniformly accelerated motion and the concept of free fall under gravitational acceleration (g) are introduced. Finally, relative motion and relative velocity are explained, including formulas for objects moving in the same or opposite directions. These notes are ideal for quick revision of core mechanics principles for exams.
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Rest and Motion are relative terms, nobody can exist in a state of absolute rest or of absolute motion.
The motion of an object is said to be one dimensional motion if only one out of three coordinates specifying the position of the object change with time. In such a motion an object move along a straight line path.
The motion of an object is said to be two dimensional motion if two out of three coordinates specifying the position of the object change with time. In such motion the object moves in a plane.
The motion is said to be three dimensional motion if all the three coordinates specifying the position of an object change with respect to time ,in such a motion an object moves in space.
The path length traversed by an object between two points is not the same as the
magnitude of displacement always. The displacement depends only on the end points;
whereas the path length depends on the actual path. The two quantities are equal only if
the object does not change its direction during the course of its motion. In all other cases,
the path length is greater than the magnitude of displacement.
Average speed :-
The average speed of an object is greater than or equal to the magnitude of the averagevelocity over a given interval of time. The two are equal only if the path length is equal to
the magnitude of the displacement.
A displacement is the shortest distance from the initial to the final position of a point P. Thus, it is the length of an imaginary straight path, typically distinct from the path actually travelled by P. A displacement vector represents the length and direction of this imaginary straight path.
The magnitude of displacement is less than or equal to the actual distance travelled
by the object in the given time interval.
Displacement ? Actual distance
It is rate of change of distance covered by the body with respect to time.
Speed = Distance travelled /time taken
Speed is a scalar quantity .
Its unit is meter /sec.
Dimensional formula of speed is
[M0L1 T -1 ] . It is positive or zero but never negative.
If an object covers equal distances in equal intervals of time than the speed of the moving object is called uniform speed. In this type of motion, position – time graph is always a straight line.
The speed of an object at any particular instant of time is called instantaneous speed. In this measurement, the time ?t?0. When a body is moving with uniform speed its instantaneous speed = Average speed = uniform speed.
The rate of change of position of an object in a particular direction with
respect to time is called velocity. It is equal to the displacement covered by an
object per unit time.
Velocity =Displacement /Time
Velocity is a vector quantity
its SI unit is meter per sec.
Its dimensional formula is [M0L1 T -1 ].
It may be negative, positive or zero.
When a body moves in a straight line then the average speed and average velocity
are equal.
The rate of change of velocity of an object with respect to time is
called its acceleration.
Acceleration = Change in velocity /time taken
It is a vector quantity,
Its SI unit is meter/ sec2
Its dimension is [M0L1 T -2 ].
It may be
positive ,negative or zero.
If the velocity of an object increases with time, its acceleration is positive .
If the velocity of an object decreases with time, its
acceleration is negative . The negative acceleration is also called retardation or
deacceleration.
Formulas of uniformly accelerated motion along straight line:
In the absence of the air resistance all bodies fall with the same acceleration towards earth from a small height. This is called free fall. The acceleration with which a body falls is called gravitational acceleration (g).Its value is 9.8 m/sec2 .
The rate of change of distance of one object with respect to the
other is called relative velocity. The relative velocity of an object B with respect to the
object A when both are in motion is the rate of change of position of object B with
respect to the object A.
Relative velocity of object A with respect to object B, VAB = VA - VB When both objects are move in same direction, then the relative velocity of object B
with respect to the object A,
VBA =
VB - VA When the object B moves in opposite direction of object A .
VBA =
VB + VA
Motion in a straight line, or one-dimensional motion, occurs when only one of the three coordinates specifying an object's position changes with time.
Path length is the total distance covered by an object, while displacement is the shortest distance between the initial and final positions. Path length is always greater than or equal to the magnitude of displacement.
Average speed is the total distance traveled divided by the total time taken. It is always greater than or equal to the magnitude of average velocity.
Acceleration is the rate of change of velocity of an object with respect to time. It is a vector quantity with SI units of meter per second squared.
Negative acceleration, also known as retardation or deceleration, occurs when the velocity of an object decreases with time.
Free fall is the motion of an object falling towards Earth under gravity, in the absence of air resistance. The acceleration during free fall is gravitational acceleration (g).
The relative velocity of object B with respect to object A is given by VAB = VA - VB. If they move in opposite directions, it becomes VBA = VB + VA.
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