Nine Standard >> Some definitions related to force & motion

Definitions related to force & motion

Motion, a core principle of physics, entails the alteration of an object's position as time progresses. It is a key aspect of our everyday lives, as we observe objects moving or remaining at rest. To better understand motion, it is essential to explore two states: the state of rest and the state of motion.

The state of rest refers to an object's condition when it is not changing its position with respect to its surroundings. In other words, an object at rest remains stationary and does not exhibit any movement. It is important to note that the state of rest does not necessarily mean the absence of all motion at the microscopic level. Atoms and molecules within an object are constantly in motion, even when the object as a whole appears to be at rest.

On the other hand, the state of motion implies that an object is changing its position concerning its surroundings. This change can be described in terms of speed, direction, or both. When an object is in a state of motion, it can either move in a straight line, follow a curved path, rotate, or undergo a combination of these movements.

Displacement: In physics, displacement refers to the change in position of an object from its initial point to its final point. It is a vector quantity that takes into account both the magnitude (distance) and direction of the change in position. Displacement is often represented by an arrow indicating the direction and length, or magnitude, of the change in position.

Speed: Speed, a scalar quantity, quantifies the rate at which an object is traveling, indicating the magnitude of its motion. It is the rate at which an object covers a certain distance in a given amount of time. Speed does not consider the direction of motion and is calculated by dividing the distance traveled by the time taken.

Let Length=L
      Time=T
Dimentional formula of Speed=\(\frac{Displacement}{Time}\)
        =\(\frac{L}{T}\)
        =[\(LT^{-1}\)]

Unit of Speed= cm/s or 
                  m/s

The unit of speed is typically meters per second (m/s) in the International System of Units (SI).

Velocity: Velocity is a vector quantity that combines speed and direction. It measures the rate at which an object changes its position in a specific direction. The calculation involves dividing the object's displacement by the duration it takes to obtain the value. It is calculated by dividing the displacement of an object by the time taken.

Let Length=L
      Time=T
Dimentional formula of Velocity=\(\frac{Displacement}{Time}\)
        =\(\frac{L}{T}\)
        =[\(LT^{-1}\)]

Unit of Velocity= cm/s or 
                  m/s
 

Uniform: Uniform refers to a consistent or constant nature of motion. In the context of physics, uniform motion implies that an object is moving at a constant speed in a straight line, without any changes in velocity or acceleration. This implies that the object traverses the same distances during equivalent time intervals. Uniform motion is characterized by a steady and unvarying movement.

Acceleration: The rate of increment of velocity with respect to time is called acceleration.

Let Length=L
      Mass=M
      Time=T
      Distance=D

accleration= \(\frac{velocity}{time}\)
                = \(\frac{V}{T}\)
                = \(\frac{\frac{D}{T}}{T}\)
                = \(\frac{D}{T^{2}}\)

Dimentional formula of accleration= \(\frac{L}{T^{2}}\)
                                                   = [\(LT^{-2}\)]

Unit of accleration= cm/\(s^{2}\) or 
                                m/\(s^{2}\)

Retardation: The rate of decrement of velocity with respect to time is called accleration. If the acceleration be positive then retardation is negative acceleration.

    A body moving with uniform velocity u and after decrement of velocity, it becomes v in time t. That is u>v. So decrement of velocity is v-u. 

        So, Retardation= \(\frac{u-v}{t}\)
                               = -\(\frac{v-u}{t}\)
                               =-a [\(\because \frac{v-u}{t}\)
                                      a=acceleration ]

Dimentional formula of retardation= \(\frac{L}{T^{2}}\)
                                                   = [\(LT^{-2}\)]

Unit of retardation= cm/\(s^{2}\) or 
                                m/\(s^{2}\)

Q1. A body had an initial velocity of 36 km/hr and after 10s, its velocity becomes 72 km/hr. Find the acceleration of the body.

Solution:

 Let,  u=initial velocity=36 km/hr
           =36 \(\times \frac{5}{9}\) m/s
           =20 m/s
         v=final velocity=72 km/hr
           =72 \(\times \frac{5}{9}\) m/s
           =40 m/s
         t=time taken=10s
         a= accleration=?

\(\therefore\) a=\(\frac{v-u}{t}\)
   =\(\frac{40-20}{10}\)
   =2 m/\(s^{2}\)