contestada

A car is moving with speed 40 m/s and acceleration 4 m/s2 at a given instant. Using a second-degree Taylor polynomial, estimate how far the car moves in the next second.

Respuesta :

Answer:

the estimate distance moved by the car will be equal to 42 m

Step-by-step explanation:

Using second degree polynomial

[tex]y(t) =y_0+ y'_0(x-a)+y''_0\dfrac{(x-a)^2}{2}\\[/tex]

given,

y'₀ = 40 m/s                      y''₀ = 4 m/s²

at t = 0                              y₀ = 0

[tex]y(t) = 40\times t+ \dfrac{t^2}{2}\times 4\\y(t) = 40t+ 2 t^2[/tex]

at t =1

y(1) = 40 ×1 + 2× 1²

y(1) = 42 m

hence, the estimate distance moved by the car will be equal to 42 m