## Calculus 8th Edition

Consider the position-time relation $S(t)=\dfrac{at^2}{2}+v_0t+s_0=\dfrac{2t^2}{2}+20t=t^2+20t$ and $S(0)=0+20(0)=0$ Now, $S''(t)=2t+20; S''(0)=20$ and $S'''(t)=2; S'''(0)=2$ Now, find the second degree Taylor polynomial $T_2(x)$ for the value of $t=1$ $T_2(1)=(0) \cdot (t^0)+(20) \cdot (\dfrac{t^1}{1!})+2 \times \dfrac{t^2}{2!}(0) (t^0)+20 \times \dfrac{1^1}{1!}+2 \dfrac{1^2}{2!}=21$ m Thus, the position of the car at 1 second is 21 m . No, we cannot calculate the distance traveled using this polynomial.