Short notes in Motion in a plane

Short notes for motion in one dimension

i,j,z are the unit vector along x,y and z axis
Notes: Bold letter are used to denote vector quantity

r=xi
v=(dx/dt)i
a=dv/dt=(d²x/dt²)i
a=vdv/dr
v=u+at
s=ut+1/2at²
v²=u²+2as


r=∫vdt
v=∫adt

Short notes for motion in two dimension

r=xi +yj
v=dr/dt=(dx/dt)i + (dy/dt)j
a=dv/dt=(d²x/dt²)i+(d²x/dt²)j
a=vdv/dr
v=u+at
s=ut+1/2at²
v²=u²+2as

r=∫vdt
v=∫adt

Short notes for motion in three dimension
r=xi +yj+zk
v=dr/dt=(dx/dt)i + (dy/dt)j+(dz/dt)k
a=dv/dt=(d²x/dt²)i+(d²x/dt²)j+(d²x/dt²)k
a=vdv/dr
v=u+at
s=ut+1/2at²
v²=u²+2as


r=∫vdt
v=∫adt