# Motion in a plane

## 5. Motion with constant acceleration

• Motion in two dimension with constant acceleration we we know is the motion in which velocity changes at a constant rate i.e, acceleration remains constant throughout the motion
• We should set up the kinematic equation of motion for particle moving with constant acceleration in two dimensions.
• Equation's for position and velocity vector can be found generalizing the equation for position and velocity derived earliar while studying motion in one dimension
Thus velocity is given by equation
v=v0+at                                          (8)
where
v is velocity vector
v0 is Intial velocity vector
a is Instantanous acceleration vector

Similary position is given by the equation
r-r0=v0t+(1/2)at2                                          (9)
where r0 is Intial position vector
i,e
r0=x0i+y0j
and average velocity is given by the equation
vav=(1/2)(v+v0)                                          (10)
• Since we have assumed particle to be moving in x-y plane,the x and y components of equation (8) and (9) are
vx=vx0+axt                                          (11a)
x-x0=v0xt+(1/2)axt2                                          (11b)
and
vy=vy0+ayt                                           (12a)
y-y0=v0yt+(1/2)ayt2                                           (12b)
• from above equation 11 and 12 ,we can see that for particle moving in (x-y) plane although plane of motion can be treated as two seperate and simultanous 1-D motion with constant acceleration
• Similar result also hold true for motion in a three dimension plane (x-y-z)