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Motion in a Straight line Class 11 Notes
Â Let’s start the introduction of Motion in a straight line chapter. In this chapter, first, learn about the difference between rest and motion then types of motion and all other concepts related to this chapter. Read this article and solve allimportant questions related to motion in a straight line class 11.
Mechanics
It is the branch of physics that deals with the conditions of rest or motion of the material objects around us.
Rest
If an object does not change its position with respect to its surroundings with time, then it is known as rest.
Motion
If an object changes its position with respect to its surroundings with time, then it is known as motion.
Types of Motion

Uniform Motion in a Straight Line
An object is said to be a uniform motion if it covers equal distances in equal intervals of time, however small these time intervals may be in the fixed direction.
Important facts of Uniform Motion in a straight line
 For an object is uniform motion, no force is required to maintain its motion.
 The velocity in uniform motion does not depend on the choice of origin.
 The velocity in uniform motion does not depend on the choice of the time interval (t_{2}t_{1}).

Nonuniform motion in a straight line
An object is said to be in nonuniform motion if its velocity changes with time.
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Point object
If the position of the object changes by distances much greater than its own size in a reasonable duration of time, then the object may be regarded as a point object.
Examples: Earth can be regarded as a point object for studying its motion around the sun.
Types of motion
 One dimensional motion
If only one out of three coordinates specifying the position of the object changes w.r.t. (with respect to) time, then the motion is known as onedimensional motion. It is also called rectilinear motion.
Example:
 The motion of a freely falling body.
 The motion of a train along a straight track.
 Twodimensional motion
If only two out of three coordinates specifying the position of the object change w.r.t. (with respect to) time, then the motion is known as twodimensional motions.
Example:
 The motion of planets around the sun.
 A car moving along a zigzag path on a level road.
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 Threedimensional motion
If all the three coordinates specifying the position of the object change w.r.t. (with respect to) time, then the motion is known as the threedimensional motion.
Example:
 The motion of the aeroplane in space.
 A kite flying on a windy day.
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DistanceÂ
The length of the actual path travelled by an object is known as distance.
 SI unit of distance = metre (m)
 The CGS unit of distanced = centimetre (cm)
 It is a scalar quantity because it has only magnitude and no direction.
 It can never be zero or negative during the motion of an object.
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Displacement
The displacement of an object is the change in the position of an object in a fixed direction.
 Its SI unit metres.
 The CGS unit of displacement = centimetre (cm)
 Displacement is a vector quantity because it has both magnitude and direction.
 The displacement of a body in a given time can be positive, zero or negative.
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Properties of Displacement
 Displacement is not dependent on the choice of the origin (O) of the position coordinates.
 The magnitude of the displacement of an object between two positions gives the shortest distance between these positions.
 Displacement of an object between two given positions is independent of the actual path followed by the object is moving from one position to another.
 The actual distance travelled by an object in a given time interval is greater than or equal to the magnitude of the displacement.
 The displacement of an object between two positions does not give any information regarding the shape of the actual path followed by the object between these two positions.
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Speed
The rate of change of position of an object with time in any direction is known as its speed.
 SI unit of speed = m/s
 The dimensional formula of speed = M^{0}LT^{1}
 Speed is a scalar quantity.
Types of Speed
Uniform Speed
If an object covers equal distances in equal intervals of time, then its speed is known as speed.
Nonuniform speed
If an object covers unequal distances in equal intervals of time and viceversa then its speed is known as nonuniform speed. It is also called variable speed.
Average speed
It is defined as the total distance travelled divided by the total time taken.
Average speed = Total distance/Total time
Instantaneous speed
If a body is travelling at various speeds, then its speed at a given instant of time is known as its instantaneous speed.
Velocity
The rate of change of position of an object with time in a given direction is known as its velocity.
Velocity = Displacement/Time
 SI unit of velocity = m/s
 The CGS unit of velocity = cm/s
 Dimensional formula of velocity =[M^{0}LT^{2}]
 Velocity has both magnitude and direction; hence velocity is a vector quantity.
 The velocity of a body can be positive, zero or negative.
Types of Velocity
Uniform Velocity
When a body undergoes equal displacements in equal intervals of time, then it is said to be moving with a uniform velocity.
Variable Velocity
When a body undergoes unequal displacements in equal intervals of time, then it is said to be moving with a nonuniform velocity. It is also known as nonuniform velocity.
Average Velocity
The ratio of the total displacement to the total time taken is known as average velocity.
Relative Velocity
The relative velocity of one body with respect to another body is the time rate of change of relative position of one body with respect to another body.
V_{AB} = V_{A} â€“ V_{B}
If relative velocity is in onedimensional motion, we can treat vectors as scalars just by assigning the positive sign to one direction and negative to others.
Relative velocity
The relative velocity of object 2 with respect to object 1, when both are in motion, is the time rate of changes of the position of object 2 with respect to that object 1.
Instantaneous Velocity
The velocity of an object at a particular instant of time or a particular point of its path is known as its instantaneous velocity.
Acceleration
It is defined as the change of velocity divided by the total time taken.
Acceleration = Change in velocity/Time taken
 SI unit of acceleration = m/s^{2}
 CGS unit of acceleration = cm/s^{2}
 Dimensional formula = [M^{0}LT^{2}]
 Acceleration is a vector quantity because it has both magnitude and direction.
Types of acceleration
 Uniform acceleration
If a body is moving with uniform acceleration, it means that the change in velocity is equal for an equal interval of time.
 Nonuniform acceleration
If a body is moving with nonuniform acceleration, it means that the change in velocity is unequal for an equal interval of time.
 Average acceleration
A body moving with variable velocity, the average acceleration is defined as the ratio of the total change in velocity of the body to the total time interval taken.
 Instantaneous acceleration
The acceleration of an object at a given instant of time or a given point of its motion is known as its instantaneous acceleration.
NOTE:
Positive acceleration: If the velocity of a body increases with time, its acceleration is positive (+ve).
Negative acceleration: If the velocity of an object decreases with time, its acceleration is negative (ve).
Equation of Motion in a straight line
Let a car starts with initial velocity (u) and after the time (t) its velocity changes to (V) which is the final velocity of the car, if the uniform acceleration of a car is (a) and the distance travelled in time (t) is (s), then the following formulae are made, which are called the equations of uniformly accelerated motion.
 v = u + at
 s = ut + Â½ at^{2}
 v^{2} = u^{2} + 2as
 Distance travelled in nth second.
S_{n} = u + a/2 (2n1)
When an object moves with uniform acceleration (a) and velocity changes from u to v in a time interval (t), then the velocity at the midpoint of its path
= /2
Motion under Gravity
Equation of motion for a freely falling object
 V = u + gt
 S = ut + Â½ gt^{2}
 V^{2} = u^{2} + 2gs
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Note:
 When an object falls freely under the action of gravity, its velocity increases and the value of g is taken positively.
 When an object is thrown vertically upward, its velocity decreases and the value of g is taken negatively.
 When an object is dropped freely from the top of the tower and another object is projected horizontally from the same point, both will reach the ground at the same time.
 A body is dropped from a tower a height (h) and it reaches after (t) seconds on earth. From the same tower if 2 objects are thrown (one upward and the other downwards) with the same velocity u and reach the earth surface after t_{1} and t_{2} seconds respectively then
Â Â Â Â Â Â Â T = âˆšt_{1}t_{2}
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