Introduction to Kinematics

Kinematics: It is the branch of mechanics that deals with the study of motion of objects is called Kinematics. It doesn’t account for the cause of motion of the body.

Rest: A body is said to be in motion if it doesn’t change its position with time.

Motion: A body is said to be in motion if it changes it position with time in respect to surrounding.

Motion and Rest are relative terms. A body can be at motion with respect to one object and even in motion with respect to another object at the same time.

Some terms regarding motion:

Distance: The actual length of path covered by the body is called distance.

Displacement: The shortest distance covered by the body between two points is called displacement.

Differences between Distance and Displacement:

Remember:

  • Distance always increases with time but displacement may increase or decreases with time.
  • Displacement and distance have same unit.
  • Displacement can never be greater than the distance.

Speed:
The distance travelled by the body in one second is called speed.

Mathematically,
$$\text{Speed} =\frac {\text{Distance travelled}}{\text{Time taken}} $$

  • Uniform Speed: If a body covers equal distance in equal interval of time, the body is said to be in uniform speed. Example: If a body travels a distance of 20 metres in 1 second, then it travels 40 metres in 2 seconds.
  • Average Speed: It is the ratio of total distance travelled to total time taken in travelling a certain distance.
  • Instantaneous speed: It is speed of any object at a particular instant of time.

Velocity: The rate of change of displacement with respect to time is called velocity.

Mathematically, $$\text{Speed} =\frac {\text{Displacement}}{\text{Time taken}} $$

  • Uniform Velocity: If a body covers equal displacement in equal interval of time. The body is said to be in uniform velocity.
    Example: A uniform body has displacement of 200 metres in one minute 400 metres in two seconds.
  • Non-Uniform Velocity: A body is said to have non uniform velocity, if it covers unequal displacement in equal interval of time.
    Example: A body has dispacement of 200 metres in one minute and 300 metres in two minute.
  • Instantaneous Velocity: The velocity of a body at a particular instant is called instantaneous velocity. Mathematically,  $$ v = \lim_{ \Delta t  \to 0} \frac{ \Delta s}{ \Delta t} =  \frac{ds}{dt} $$

Differences between speed and velocity:

Acceleration: The rate of change of velocity is called acceleration.

  • Average Acceleration: The average rate of change of velocity is called average acceleration. Mathematically, $$\text{Average acceleration} (a_v)=\frac {\text{Final velocity (v}_2)-\text{Initial velocity(v}_1)}{\text{Final time (t}_2)-\text{Initial time(}\text{t}_1)} $$
  • Instantaneous acceleration: The acceleration of a body at any instant is called instantaneous acceleration. $$a = \lim_{ \Delta t \to 0} \frac{ \Delta v}{ \Delta t} = \frac{dv}{dt} $$

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