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Represent position vector of a particle ...

Represent position vector of a particle in terms of velocity and acceleration vectors.

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Let `vecr_0` and `vecr` be the position vectors of the particle at time 'zero' and 't'. Let the corresponding velocities be `vecv_0` and `vecv`
The displacement `vecr-vecr_0=((vecv+vecv_0)/(2))t=((vecv_0+vecat+vecv_0)/(2))t`
`vecr-vecr_0=v_0t+1/2vecat^2`
`:.` Position vector `vecr=vecr_0+v_0t+1/2vecat^2`
The x and y components are x=`x_0+(v_0)_xt+1//2a_xt^2` and
`y=y_0+(v_0)_yt+1//2_yt^2`
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