Determination of velocity and acceleration from s-t graph

Question

Suppose , a particle is moving away with constant acceleration . It passes distance s by time t . A chart of their values is given in the following :

$$\begin{array}{|l|l|l|l|l|l|l|} \hline t & 0 & 1 & 3 & 6 & 8 & 10\\ \hline s & 0 & 10 & 42 & 120 & 192 & 280\\ \hline \end{array}$$

I have drawn a graph of t in x-axis and s in y-axis .The graph is as follows :

I want to determine the initial velocity and acceleration from this graph . I know that initial velocity is the velocity at time t = 0 . And we can get velocity from the slope of s-t graph . But I can't determine initial velocity and acceleration .

Answer 1

Hint: Find $v$ and $a$ using your table if $s = vt+a\frac{t^2}{2}$.