**Motion in One Dimension Physics : : Equations of Motion Under Gravity**

Mechanics can be divided into 2 Parts :

**(A) Statics :**

- Which deals with the study of stationary objects.

**(B) Dynamics :**

- Which deals with the study of moving objects.

**Terms Regarding Motion**

**Displacement :**

- The change in position of the body in a certain direction is known as displacement. It is a vector quantity.

**Distance :**

- The total path transversed by the body between initial and final states is called distance. It is a scalar quantity.
- Displacement may be positive, negative or zero but distance is always positive.

- Time rate of change of displacement is called velocity.

Velocity ( v ) = Displacement ( x ) / Time ( t ) |

- It is a vector quantity and may be positive or negative.

Average Velocity = Total Displacement / Total Time |

- Average velocity is zero, if the body returns to starting point in the given time interval.
- If the body covers first half distance with velocity V
_{1}and next half with velocity V_{2}, then

Average Velocity = 2 V_{1}*V_{2} / V_{1}+V_{2} |

- If a body travels with uniform velocity V
_{1}for time t_{1}and with uniform velocity V_{2}for time t_{2}, then

Average Velocity = V_{1}t_{1} + V_{2}t_{2} / t_{1}+t_{2} |

**Speed :**

- It is a scalar form of velocity and is defined as the distance traveled in 1s.
- If the body covers a distance d in time t, then

v = d / t ( or ) Average Speed = Total Distance / Total Time |

- If the body covers first half distance with speed u and next half with speed v, then

Average Speed = 2uv / u+v |

**Acceleration :**

- Time rate of change of velocity is known as acceleration.
- It is a vector quantity. If Δ v is the change in velocity in time Δt, then

α = Δ v / Δ t |

- Negative acceleration is known as retardation. It indicates that the velocity of the object is decreasing with respect to time.
- Acceleration is uniform when neither its direction nor magnitude changes with respect to time.

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