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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)


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