VC1.2

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Given, $r = 3 i - 6 t 2 j + 4 t k$

Since i,j,k are constant vectors, $\frac{di}{dt}=\frac{dj}{dt}=\frac{dk}{dt}=0$

Therefore, from the given $\frac{dr}{dt}=\frac{d}{dt}(3)i-\frac{d}{dt} (6t^2) j+\frac{d}{dt} (4t) k = -12t j+4k$

From the above, $\frac{d^2 r}{dt^2}=\frac{d}{dt}[\frac{dr}{dt}]= -\frac{d}{dt} (12t) j+\frac{d}{dt} (4) k = -12j$

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