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

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