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**Soroban** Hello, riverjib!

We have: .$\displaystyle \frac{d^2r}{dt^2} \;=\;-(i+j+k)$

Integrate: .$\displaystyle \frac{dr}{dt} \;=\;-(i+j+k)t + C_1$

We are told that, when $\displaystyle t = 0,\:\frac{dr}{dt} = 0$

. . So we have: .$\displaystyle -(i+j+k)0 +C_1 \:=\:0\quad\Rightarrow\quad C_1 = 0$

Hence: .$\displaystyle \frac{dr}{dt} \:=\:-(i+j+k)t$

Integrate: .$\displaystyle r(t) \;=\;-\frac{1}{2}(i+j+k)t^2 + C_2$

We are told that, when $\displaystyle t = 0,\:r = 10i + 10j +10k$

. . So we have: .$\displaystyle -\frac{1}{2}(i+j+k)0^2 + C_2 \:=\:10i + 10j + 10k\quad\Rightarrow\quad C_2\:=\:10i + 10j + 10k$

Therefore: .$\displaystyle \boxed{r(t) \;=\;-\frac{1}{2}(i+j+k)t^2 + 10(i+j+k)}$