How are displacement, velocity and acceleration related?

1 Answer
Jul 29, 2015

Answer:

The displacement (#x#), velocity (#v#) and acceleration (#a#) are related by a set of simple equations and are called the kinematic equations. I am writing them below.

Explanation:

Assuming that acceleration is uniform and the motion is rectilinear (we don't need to use vector notation then), the equations are,

#v = v""_0 + at#

#v^2 = v""_0^2 + 2a(x-x""_0)#

#x = x""_0 + v""_0t + 1/2at^2#

Where symbols have their usual meanings.

If the motion is on a plane or in space, we need to use vector notations or different equations for each of the coordinate axes.
And if acceleration is a function of time and is not constant, the equations get a little complicated. Two important results to find position vector and velocity vector are given below,

#vecr(t) = vecr""_0 + int_0^t vecv(t)dt# , where, #vecr""_0# is the initial position vector.

#vecv(t) = vecv""_0 + int_0^t veca(t)dt#, where #vecv""_0# is the initial velocity vector.

Here, #veca(t)# denotes that the acceleration vector is not constant but is a function of time.