Answer
21 m and NO
Work Step by Step
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.
