Answer
$s(t)=4.9t^2+5t+10$
Work Step by Step
Here, $s=\dfrac{ds}{dt}=9.8t+5$, thus the general form of the function is: $s(t)=4.9t^2+5t+C$
Since we have $s(0)=10$
Therefore, $s(0)=10 \implies 10=4.9(0)^2+5(0)+C$
Thus, $C=10$
Hence, $s(t)=4.9t^2+5t+10$