Kinematics

Kinematics

 It deals with the motion of objects without taking into account the cause of motion.

Distance and Displacement

Uniform Motion:

Uniformly Accelerated Motion

Uniformly Retarded Motion
"Angle made by resultant velocity"

Types of Motion: Motion of the body can be three types

 [a]Translatory

 [b] rotational

 [c] Vibrational

It can also be classified as 1 dimensional, 2 dimensional or 3 dimensional

Distance is the actual path covered by the particle, while directional distance between initial and final position is called displacement. Distance is a scalar quantity and displacement is a vector quantity.

[a] the magnitude of the displacement is equal to the minimum possible distance between the two points.

Distance less then equal to |displacement|

[b] For moving particle distance never decreases with time while the displacement can decrease with time implying that the body is moving towards the initial point,

[c] For moving particle distance is always greater than zero whereas displacement can be positive negative or zero. Thus, a body may cover distance without having displacement but a body does not have displacement without covering distance.

Motion In One dimension: In motion of the particle we come across the terms distance, displacement, speed, velocity, acceleration and time. Of these quantities velocity, acceleration and displacement are treated as vectors. Motion in one dimension can be classified into following categories

[a] uniform motion

[b] uniformly accelerated motion

[c]Uniformly retarded motion

[d] Uniformly retarded and then accelerated in opposite direction

[e] Non uniformly accelerated or retarded motion

In uniform motion the velocity of the particle I constant, therefore acceleration is zero. Thus

S=v t

Uniform motion is possible in one dimensional motion only, as if the direction is changing the velocity will also change Moreover in uniform motion average and instantaneous values of speed and velocity are equal.

In uniform acceleration, the acceleration of the body is assumed to be equal in magnitude and direction. In one dimensional motion we also assume the acceleration to be parallel to the initial velocity. The equation of motion for uniformly accelerated motion are

[a] v = u + at

[b]v² = u² + 2aS

[c] S = ut + at²/2

[d] S_nth = u + a(2n-1)/2

In kinematics there are 5 variables u, v, a, t and s. if we know the value of 3 variables we can find the other 2 using these two equations.

In this case the initial velocity can’t be zero. The acceleration is constant in magnitude and direction and opposite to the direction of the velocity. The following equations are used in this case.

[a] v= u – at

[b] v² = u² – 2 aS

[c] s = ut – at²/2

[d] s_nth= u - a(2n-1)/2

Non Uniformly Accelerated Motion or Retarded Motion:

When acceleration of the particle is not constant, we go for basic equations of velocity and acceleration i.e.

[a] v = ds/dt       or   ds = vdt

[b] a = dv/dt     or    dv = a dt

[c] a = v dv/ds  or    vdv= ads

Using differentiation

s – t equationàv-t equation àa-t equation

Using integration with boundary conditions

a-t equation àv-t equation às-t equation

Average Speed: The average speed is defined as the ratio of the total distance traveled by the body to the total time taken.

[1] if a particle travels distances s₁,s₂,s₃………….. with velocities v₁,v₂,v₃………… then

v_av= ∆S/∆t=∑si/∑(si/vi)

If s₁=s₂=…….s_n=s, then