# Terms Regarding Motion

## Terms Regarding Motion

Motion and rest are relative terms. They depend on the situation of the observer and the observer and the object being observed. So rest and motion can be described with respect to the observer. The branch of mechanics which deals with the body at rest is called static. The branch of physics which deals with motion without knowing its cause is known as kinematics.

## Distance

The length of the actual path followed by a body in moving from initial position to final position is known as distance. Its S.I unit is the meter (m). It is a scalar quantity.

## Displacement

The shortest distance between the initial and final position of a body is known as displacement. Its SI unit is the meter (m). It is a vector quantity.

**Difference between distance and displacement**

S.N |
Distance |
Displacement |

1 |
Distance is the length of the actual path travelled by an object. |
Displacement of an object is the shortest length from the initial position to the final position of an object. |

2. |
Distance travelled by an object is always positive. |
Displacement may be positive, negative or zero. |

3. |
Distance travelled depends on upon the shape of the path followed by an object. |
Displacement does not depend upon the shape of the path followed by an object. |

4. |
Distance is a scalar quantity. |
Displacement is a vector quantity. |

## Speed

The rate of change of distance is known as speed. In other words, distance travelled by a body in unit time is called speed. Its SI unit is m/s. It is a scalar quantity.

Mathematically,

$$\text {Speed} = \frac {distance travelled}{time taken} $$

## Velocity

The rate of change of displacement is known as velocity. Its unit is m/s. It is the vector quantity.

Mathematically,

$$\text {Speed} = \frac {distance travelled}{time taken} $$

**Difference between Speed and Velocity**

S.N |
Speed |
Velocity |

1. |
It is the distance travelled by the body per unit time. |
It is the rate of change of displacement. |

2. |
Speed is always positive. |
Velocity may be positive, negative or zero. |

3. |
Speed of a body is equal to or greater than the velocity of the body. |
Velocity of a body is equal or less than the speed of the body. |

4. |
Speedis a scalar quantity. |
Velocityis a vector quantity. |

### Uniform and non-uniform speed

A body is said to have uniform speed if it travels the equal distance in equal intervals of time. Otherwise, the body is said to have non-uniform speed.

### Uniform and non-uniform velocity

A body is said to have uniform velocity if it covers equal displacement in equal intervals of time.Otherwise, the body is said to have non-uniform velocity.

### Instantaneous velocity

When the velocity of the body continuously changes, we have to define velocity at a particular instant of time. Such velocity is known as instantaneous velocity. Mathematically, it is the ratio of displacement covered by a body to a very small time method.

$$\begin{align*}\text {i.e. Instantaneous velocity} (v) &= \lim {\Delta t \to o} \frac {\Delta s}{\Delta t} \\ &= \frac {ds}{dt} \\ \end{align*}$$

### Average speed and velocity

Average speed is defined as the ratio of total distance travelled to total time taken.Average velocity is defined as the ratio of total displacement covered to total time taken.

$$\begin{align*} V_{av} &= \frac {\text {total displacement}}{\text {total time}} \\ &= \frac {s_1 - s_2}{t_2 - t_2} =\frac {\Delta s}{\Delta t} \end{align*}$$

### Acceleration

Acceleration is defined as the rate of change of velocity with respect to time. Let the initial velocity of an object is u and it becomes v in time interval t. Then the average acceleration is

$$\begin{align*} a &= \frac {\Delta v}{\Delta t} = \frac {v - u}{t} \\ at &= u - v \\ \text {or} \: v &= u + at \end{align*}$$

### Deceleration

Retardation is the rate of decrease of velocity. Since the final velocity is smaller than the initial velocity, the acceleration becomes negative and decelaration is negative acceleration.

### Uniform acceleration

An object is said to be moving with a uniform acceleration if its velocity change by the equal amount in equal interval f time. Acceleration due to gravity is an example of uniform acceleration.

### Variable acceleration

An object is said to be moving with a variable acceleration if the velocity change in equal time interval is not same.

### Average acceleration

The average acceleration of the object for the given motion is defined as the ratio of the total change in velocity of the acceleration of the object for the given motion is defined as the ratio of the total change in velocity of the object to the total time interval.

Consider an object moving along a straight line from P to Q as shown in the figure. At P, the velocity is v_{1} at time t_{1} and at Q, the velocity is v_{2} at time t_{2}.

$$Then\; change \;in \;velocity = v_2 – v_1 = \Delta v $$

$$ and \;change\; in \;time = t_2 – t_1 = \Delta t$$

$$\therefore average acceleration a_{av} \;= \frac {total change in velocity} {total time interval} $$

$$= \frac {\Delta v}{\Delta t}$$

### Instantaneous acceleration

If the velocity of a body is changing continuously with respect to time, we define acceleration at particular instant of time or at a point on its path as the instantaneous acceleration and it is given by the limiting value of \(\frac {\Delta v}{\Delta t} \) when \(\Delta t\) tends to zero.

$$\begin{align*} \therefore \text {instantaneous acceleration,} a &= \lim {\Delta t \to \theta \frac {\Delta v}{\Delta t} = \frac {dv}{dt} \end{align*}$$

Acceleration is a vector quantity and its unit is ms^{-2} in SI-units and cm^{-2} in CGS-system.

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