A particle moves on a line by $\mathrm{S}={\mathrm{at}}^2+\mathrm{bt}+\mathrm{c}.$ If the displacement after 1 second is 16 cm. The
velocity of after 2 seconds is 24 cm/sec and the acceleration is $8\mathrm{cm}/{\sec }^2$ then (a,b,c)=

$$\begin{gathered} \mathrm{S}={\mathrm{at}}^2+\mathrm{by}+\mathrm{c} \\ \mathrm{t}=1 \mathrm{S}=16 \Rightarrow \mathrm{a}+\mathrm{b}+\mathrm{c}=16 -\left(1\right) \\ \mathrm{V}=\frac{\mathrm{ds}}{\mathrm{dt}}=2\mathrm{at}+\mathrm{b} \\ \mathrm{t}=2 \mathrm{V}=24 \Rightarrow 4\mathrm{a}+\mathrm{b}=24 -\left(2\right) \\ \mathrm{a}=\frac{\mathrm{dv}}{\mathrm{dt}}=2\mathrm{a}=8 \Rightarrow \mathrm{a}=4 \end{gathered}$$

fromer (2) $\Rightarrow \mathrm{b}=24-16=8$

fromer (1) $\Rightarrow 4+8+\mathrm{c}=16 \Rightarrow \mathrm{c}=4$