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**Motion in a Straight line Class 11 Notes**

** 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 all-important 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}).

**Non-uniform motion in a straight line**

An object is said to be in non-uniform 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 one-dimensional motion. It is also called rectilinear motion.

**Example:-**

- The motion of a freely falling body.
- The motion of a train along a straight track.

**Two-dimensional 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 two-dimensional motions.

**Example:-**

- The motion of planets around the sun.
- A car moving along a zigzag path on a level road.

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**Three-dimensional 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 three-dimensional motion.

**Example:-**

- The motion of the aeroplane in space.
- A kite flying on a windy day.

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**Distance **

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.

**Non-uniform speed**

If an object covers unequal distances in equal intervals of time and vice-versa then its speed is known as non-uniform 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 non-uniform velocity. It is also known as non-uniform 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} – **V**_{B}

If relative velocity is in one-dimensional 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.

**Non-uniform acceleration**

If a body is moving with non-uniform 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 + ½ at**^{2}**v**^{2}= u^{2}+ 2as- Distance travelled in nth second.

**S _{n} = u + a/2 (2n-1)**

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 + ½ 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

** T = √t _{1}t_{2}**

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**I hope you like this post “motion in a straight line”. Comment below for other important chapter notes.**

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