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If a body does not change its position with respect to time and the surroundings, it is said to be at rest and else it is said to be in motion. Motion of objects can take place along one direction, two directions or three directions at a time.

If an object moves along a straight path it is said to be linear or one-dimensional motion. If an object moves along two directions at a time like that of a ball hit for a sixer in a cricket, it is two-dimensional. The haphazard motion of a honey bee can be three-dimensional.

The change in position of an object is termed displacement. It requires both direction and magnitude for its complete description and hence such physical quantities are called a vectors. The length of the path covered by a moving body is its distance and is independent of direction. Thus, such physical quantities are called scalars.

The rate of distance covered by a body is its speed and is measured in metre per second in international units. If a body covers equal distances in equal intervals of time however small the intervals may be, it has uniform speed. If a body covers unequal distances in equal intervals or equal distances in unequal intervals then it is said be moving with non-uniform speed.

• Speed is a scalar quantity.

• Speed = $\frac{\text{distance travelled}}{\text{Time taken.}}$ .

• A body is said to be moving with uniform speed if it has equal intervals of time, however small these intervals may be.

• A body is said to be moving with non uniform speed if it has unequal distances in equal intervals of time or equal distances in unequal intervals of time, however small these intervals may be.

**Average speed:**

• Average speed = $\frac{\text{total distance travelled}}{\text{total time taken}}$

• Instantaneous speed = $\underset{\u2206t\to \text{0}}{\text{lim}}\frac{\u2206\text{s}}{\u2206\text{t}}$= $\frac{\text{ds}}{\text{dt}}$.

• If a particle covers the 1^{st} half of the total distance with a speed 'a' and the second half with a speed 'b'

Average speed = $\frac{\text{2ab}}{\text{a+b}}$ .

• If a particle covers 1^{st} 1/3^{rd} of the total distance with a speed 'a', 2^{nd }1/3^{rd} of the distance with a speed 'b' and 3^{rd} 1/3^{rd} of the distance with speed 'c'

Average speed = $\frac{\text{3abc}}{\text{ab+bc+ca}}$ .

• 1 kmph = $\frac{\text{5}}{\text{18}}$ ms^{-1} ; 1mph = $\frac{\text{22}}{\text{15}}$ fts^{-1}

• For a body with uniform speed, distance travelled = speed x time.

The rate of displacement of a body is its velocity and is measured in metre per second in international units. If a body has equal displacements in equal intervals of time however smaller the intervals may be, it is said to be moving with uniform velocity. If the body is moving such that it has unequal displacements in equal intervals or equal displacements in unequal intervals of time, it is said to be moving with non-uniform velocity. The ratio of total displacement to total time taken by the body gives its average velocity. The velocity of a body at a given instant is its instantaneous velocity.

• Velocity is a vector quantity.

• For a body moving with uniform velocity , the displacement is directly proportional to the time interval.

• If the direction or magnitude or both of the velocity of a body change, then the body is said to be moving with non-uniform velocity** .**

• Average velocity** **= $\frac{\text{Net displacement}}{\text{Total time taken}}$

• For a body moving with uniform acceleration, the Average velocity = $\frac{\text{u+v}}{\text{2}}$.

• The velocity of a particle at any instant of time or at any point of its path is called instantaneous velocity $\overrightarrow{\text{v}}$ = $\underset{\u2206t\to \text{0}}{\text{lim}}\frac{\u2206\overrightarrow{\text{s}}}{\u2206\text{t}}=\frac{\text{d}\overrightarrow{\text{s}}}{\text{dt}}$ .

**Average Velocity:**

• If a particular under goes a displacement s_{1} along a straight line t_{1} and a displacement s_{2} in time t_{2} in the same direction, then

Average velocity = ($\frac{{\text{s}}_{}}{}$_{1}_{ } _{2}_{1}_{ }_{2}_{ }

• If a particle undergoes a displacement s_{1} along a straight line with velocity v_{1} and a displacement s_{s} with velocity v_{2} in the same direction, then

Average velocity = $\frac{\text{(}{\text{s}}_{}}{}$_{1}_{ } _{2}_{ }_{1}_{ }_{2}_{ }_{1}_{ }_{2}_{ }

• If a particle travels first of the displacement along a straigh line with velocity v_{1} and the next half of the displacement with velocity v_{2} in the same direction , then

Average velocity = $\frac{\text{2}{\text{v}}_{\text{1}}{\text{v}}_{\text{2}}}{{\text{v}}_{\text{2}}\text{+}{\text{v}}_{\text{1}}}$ (in the case(b) put s_{1} = s_{2})

• If a particle travels for a time t1 with velocity v1 and for a time and for a time t2 with velocity v2 in the same direction, then

Average velocity = $\frac{{\text{v}}_{\text{1}}{\text{t}}_{\text{1}}\text{+}{\text{v}}_{\text{2}}{\text{t}}_{\text{2}}}{{\text{t}}_{\text{1}}\text{+}{\text{t}}_{\text{2}}}$ .

• If a particle travels first half of the time with velocity v_{1} and the next half of the time with velocity v_{2} in the same direction, then

Average velocity = $\frac{{\text{v}}_{\text{1}}\text{+}{\text{v}}_{\text{2}}}{\text{2}}$ (in the case d put t_{1} = t_{2}) .

• Velocity of a particle is uniform if both it magnitude and direction remains unchanged.

• Velocity of a body changes when magnitude or direction or both change.

**Acceleration**

The rate of change in velocity is called acceleration and is measured in metre per square second in the international system of units.

Acceleration, a = $\frac{\text{Final velocity - Initial velocity}}{\text{Time}}$

**Note:** The negative acceleration is termed as retardation.

**Differences Between Distance and Displacement **

S.No. |
DISTANCE |
DISPLACEMENT |

1. | It is defined as the actual path traversed a body | It is the shortest distance betweeen two points by between which the body moves. |

2. | It is a scalar quantity. | It is a vector quantity. |

3. | It can never be a negative or zero. | It can be negative, zero or positive. |

4. | Distance can be equal to or greater than displacement. | Distance can be egaual to or less than distance. |

5. | Distance travelled is not a unique path between two points. | Displacement is a unique path between two points. |

6. | The distance between two points gives full information of the types of path followed by the body. | Displacement between two points does not give full information of the types of path followed by the body. |

7. | Distance never decreases with time. For a moving body, it is never zero. | Displacement can decrease with time. For a moving body, it can be zero. |

8. | Distance in SI is measured in metre. | Displacement in SI is measured in metre. |

S.No. |
SPEED |
VELOCITY |

1. | It is defined as the rate of change of distance. | It is defined as the rate of change of displacement. |

2. | It is a scalar quantity. | It is a vector quantity. |

3. | It can never be negative or zero. | It can be negative,zero or posituve. |

4. | Speed is velocity without direction. | Velocity is directed speed. |

5. | Speed may or may not be equal to velocity. | A body may possess different velocities but the same speed. |

6. | Speed never decreases with time. For a moving body, it is never zero. | Velocity can decrease with time. For a moving body , it can be zero. |

7. | Speed in SI is measured in ms^{-1} |
Velocity in SI, is measured in ms^{-1} |

If a body does not change its position with respect to time and the surroundings, it is said to be at rest and else it is said to be in motion. Motion of objects can take place along one direction, two directions or three directions at a time.

If an object moves along a straight path it is said to be linear or one-dimensional motion. If an object moves along two directions at a time like that of a ball hit for a sixer in a cricket, it is two-dimensional. The haphazard motion of a honey bee can be three-dimensional.

The change in position of an object is termed displacement. It requires both direction and magnitude for its complete description and hence such physical quantities are called a vectors. The length of the path covered by a moving body is its distance and is independent of direction. Thus, such physical quantities are called scalars.

The rate of distance covered by a body is its speed and is measured in metre per second in international units. If a body covers equal distances in equal intervals of time however small the intervals may be, it has uniform speed. If a body covers unequal distances in equal intervals or equal distances in unequal intervals then it is said be moving with non-uniform speed.

• Speed is a scalar quantity.

• Speed = $\frac{\text{distance travelled}}{\text{Time taken.}}$ .

• A body is said to be moving with uniform speed if it has equal intervals of time, however small these intervals may be.

• A body is said to be moving with non uniform speed if it has unequal distances in equal intervals of time or equal distances in unequal intervals of time, however small these intervals may be.

**Average speed:**

• Average speed = $\frac{\text{total distance travelled}}{\text{total time taken}}$

• Instantaneous speed = $\underset{\u2206t\to \text{0}}{\text{lim}}\frac{\u2206\text{s}}{\u2206\text{t}}$= $\frac{\text{ds}}{\text{dt}}$.

• If a particle covers the 1^{st} half of the total distance with a speed 'a' and the second half with a speed 'b'

Average speed = $\frac{\text{2ab}}{\text{a+b}}$ .

• If a particle covers 1^{st} 1/3^{rd} of the total distance with a speed 'a', 2^{nd }1/3^{rd} of the distance with a speed 'b' and 3^{rd} 1/3^{rd} of the distance with speed 'c'

Average speed = $\frac{\text{3abc}}{\text{ab+bc+ca}}$ .

• 1 kmph = $\frac{\text{5}}{\text{18}}$ ms^{-1} ; 1mph = $\frac{\text{22}}{\text{15}}$ fts^{-1}

• For a body with uniform speed, distance travelled = speed x time.

The rate of displacement of a body is its velocity and is measured in metre per second in international units. If a body has equal displacements in equal intervals of time however smaller the intervals may be, it is said to be moving with uniform velocity. If the body is moving such that it has unequal displacements in equal intervals or equal displacements in unequal intervals of time, it is said to be moving with non-uniform velocity. The ratio of total displacement to total time taken by the body gives its average velocity. The velocity of a body at a given instant is its instantaneous velocity.

• Velocity is a vector quantity.

• For a body moving with uniform velocity , the displacement is directly proportional to the time interval.

• If the direction or magnitude or both of the velocity of a body change, then the body is said to be moving with non-uniform velocity** .**

• Average velocity** **= $\frac{\text{Net displacement}}{\text{Total time taken}}$

• For a body moving with uniform acceleration, the Average velocity = $\frac{\text{u+v}}{\text{2}}$.

• The velocity of a particle at any instant of time or at any point of its path is called instantaneous velocity $\overrightarrow{\text{v}}$ = $\underset{\u2206t\to \text{0}}{\text{lim}}\frac{\u2206\overrightarrow{\text{s}}}{\u2206\text{t}}=\frac{\text{d}\overrightarrow{\text{s}}}{\text{dt}}$ .

**Average Velocity:**

• If a particular under goes a displacement s_{1} along a straight line t_{1} and a displacement s_{2} in time t_{2} in the same direction, then

Average velocity = ($\frac{{\text{s}}_{}}{}$_{1}_{ } _{2}_{1}_{ }_{2}_{ }

• If a particle undergoes a displacement s_{1} along a straight line with velocity v_{1} and a displacement s_{s} with velocity v_{2} in the same direction, then

Average velocity = $\frac{\text{(}{\text{s}}_{}}{}$_{1}_{ } _{2}_{ }_{1}_{ }_{2}_{ }_{1}_{ }_{2}_{ }

• If a particle travels first of the displacement along a straigh line with velocity v_{1} and the next half of the displacement with velocity v_{2} in the same direction , then

Average velocity = $\frac{\text{2}{\text{v}}_{\text{1}}{\text{v}}_{\text{2}}}{{\text{v}}_{\text{2}}\text{+}{\text{v}}_{\text{1}}}$ (in the case(b) put s_{1} = s_{2})

• If a particle travels for a time t1 with velocity v1 and for a time and for a time t2 with velocity v2 in the same direction, then

Average velocity = $\frac{{\text{v}}_{\text{1}}{\text{t}}_{\text{1}}\text{+}{\text{v}}_{\text{2}}{\text{t}}_{\text{2}}}{{\text{t}}_{\text{1}}\text{+}{\text{t}}_{\text{2}}}$ .

• If a particle travels first half of the time with velocity v_{1} and the next half of the time with velocity v_{2} in the same direction, then

Average velocity = $\frac{{\text{v}}_{\text{1}}\text{+}{\text{v}}_{\text{2}}}{\text{2}}$ (in the case d put t_{1} = t_{2}) .

• Velocity of a particle is uniform if both it magnitude and direction remains unchanged.

• Velocity of a body changes when magnitude or direction or both change.

**Acceleration**

The rate of change in velocity is called acceleration and is measured in metre per square second in the international system of units.

Acceleration, a = $\frac{\text{Final velocity - Initial velocity}}{\text{Time}}$

**Note:** The negative acceleration is termed as retardation.

**Differences Between Distance and Displacement **

S.No. |
DISTANCE |
DISPLACEMENT |

1. | It is defined as the actual path traversed a body | It is the shortest distance betweeen two points by between which the body moves. |

2. | It is a scalar quantity. | It is a vector quantity. |

3. | It can never be a negative or zero. | It can be negative, zero or positive. |

4. | Distance can be equal to or greater than displacement. | Distance can be egaual to or less than distance. |

5. | Distance travelled is not a unique path between two points. | Displacement is a unique path between two points. |

6. | The distance between two points gives full information of the types of path followed by the body. | Displacement between two points does not give full information of the types of path followed by the body. |

7. | Distance never decreases with time. For a moving body, it is never zero. | Displacement can decrease with time. For a moving body, it can be zero. |

8. | Distance in SI is measured in metre. | Displacement in SI is measured in metre. |

S.No. |
SPEED |
VELOCITY |

1. | It is defined as the rate of change of distance. | It is defined as the rate of change of displacement. |

2. | It is a scalar quantity. | It is a vector quantity. |

3. | It can never be negative or zero. | It can be negative,zero or posituve. |

4. | Speed is velocity without direction. | Velocity is directed speed. |

5. | Speed may or may not be equal to velocity. | A body may possess different velocities but the same speed. |

6. | Speed never decreases with time. For a moving body, it is never zero. | Velocity can decrease with time. For a moving body , it can be zero. |

7. | Speed in SI is measured in ms^{-1} |
Velocity in SI, is measured in ms^{-1} |

Activity 1phet.colorado has created an excellent java applet to describe the motion with respect to the position, displacement and acceleration. Using this we can recor the motion and also can replay the recorded motion.Go to ActivityActivity 2walter-fendt.de has created the Java applet that shows a car moving with constant acceleration. Using this Java applet we can vary the values of initial position, initital velocity and acceleration. We choose the option "Slow motion". Three diagrams illustrate the motion of the vehicle Position x versus time t Velocity v versus time t Acceleration a versus time tGo to Activity