Kinematics

Kinematics

    By definition, kinematics is the study of motion that neglects what causes the motion. The kinematic equations we have today are based on the idea that acceleration is held as a constant. The equations do not take into account outside factors (air resistance, friction, etc.), but they come pretty close to accurately describing the motion of an object. Take for example this differential equation:

	a=		dv/dt
	dv=		a dt
vf		tf
⌠ ⌡	dv =	⌠ ⌡	a dt
v0		ti
	vf − v0 =		aΔt
	vf =		v0 + aΔt[1].

where a is the acceleration, v is the velocity, and t is the time. It stands to reason that the final velocity of an object depends on the amount of time has passed over constant acceleration. However, we can use this equation to get something more elaborate:

v =			dx/dt
dx =			v dt = (v0 + at) dt
xf		Δt
⌠ ⌡	dx =	⌠ ⌡	(v0 + at) dt
x0		0
xf − x0 =			v0Δt + ½aΔt2
xf =			x0 + v0Δt + ½aΔt2 [1].

where x is the position. This is the equation for a object in projectile motion [1]. As you can see, projectile motion is purely a computational equation derived from basic differential equations.  Here are some examples of other kinematic equations:

x_f=x_i+(v_f+v_i)t/2

                                                   v_f²=v_i²+2aΔx [3].
    To get a better understanding of what projectile motion really is, we will explore projectile motion in the next link.
                                                                                                                                                                                          

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