**Rest And Motion**

**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**. - The terms Rest and Motion are
**relative**.

**Distance and Displacement**

**Distance:****Displacement:**The length of a straight path 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 traveled by an object to go from one point to another. | Displacement is defined as the length of the straight path 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:**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**

**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} |

**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.

**Derivation Of Equations Of Motion**

**Derivation of The Equations of Motion By Algebraic Method:**

**Derivation of S = ut + ½ at**^{2}^{}

^{2}

^{}

**Derivation of v**^{2}** – u**^{2}** = 2as**

^{2}

^{2}

**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

**(a) Velocity-time relation:**

**(ii) The equation for position-time relation:**

**(iii) Equation for position-velocity relation:**

**Conclusions From a Distance – Time Graph**