Question

A car is moving with speed 60 m/s and acceleration 4 m/s2 at a given instant. (a) using a second-degree taylor polynomial, estimate how far the car moves in the next second. m (b) would it be reasonable to use this polynomial to estimate the distance traveled during the next minute? yes no

Answer 1

Answer:

Explanation:

Using second degree taylor polynomials

let $S(t)$ be position function and set $S(0)=0$

where S(0) is the initial position

Then $v(t) = S^i(t)$ and $a(t)=S^{ii}(t)$

we have $v(0) = 60m/s$, $a(0) = 4m/s^2$

so $T_{2}(t) =S(0)+v(0)t+\frac{a(0)}{2} t^2\\\\\\=0+60t+\frac{4}{2} t^2\\\\T_{2}(t)=60t+2t^2\\\\S(1)=T_{2}(1)=60+2=62m$

b.) yes