Respuesta :
The automobile is expected to go 62 meters in the following second.
Explain the second-degree taylor polynomial?
- Quadratics are a common term used to describe degree 2 polynomials.
- A second degree Taylor polynomial at x=a is indeed the best quadratic approximation of f(x) close a, just as the tangent line to f(x) at x=a is the greatest linear approximation of f(x) near a.
Let a function in values of time reflect the location of the car:
x = f(t) ...eq 1
A second-degree Taylor polynomial can be used to estimate the position of the car in time:
x = x0 + v0/1!×t + a0/2!×t²
x = x0 + v0.t + 1/2.a0.t²
Where:
- x0 - The starting location, in meters.
- v0- The starting speed, expressed in meters per second.
- a0- The initial acceleration, expressed in m/s2.
- t- The passing of seconds.
If we are aware of, x0 = 0m, v0 = 60 m/s, t = 1 sec and a0 = 4 m/s2 , therefore the subsequent second's distance is:
x = 0 + (60).1 + 1/2.(4).1²
x = 62 m.
Thus, the automobile is expected to go 62 meters in the following second.
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