Question

The position f(x) of a particle moving in a line at various times xk is given in the following table. Estimate the velocity and acceleration of the particle at x=1.2
x f(x)
1.0 2.72
1.2 3.32
1.4 4.06
1.6 4.96
1.8 6.05
2.0 7.39
2.2 9.02

Answer 1

Answer on Question #75525 – Math – Quantitative Methods

Question

The position $f(x)$ of a particle moving in a line at various times $xk$ is given in the following table. Estimate the velocity and acceleration of the particle at $x=1.2$

x f(x)

1.0 2.72

1.2 3.32

1.4 4.06

1.6 4.96

1.8 6.05

2.0 7.39

2.2 9.02

Solution

$$v(x) = f'(x) \approx \frac{f(x+h) - f(x-h)}{2h}.$$ $$v(1.2) = f'(1.2) \approx \frac{f(1.4) - f(1.0)}{2 \cdot 02} = \frac{4.06 - 2.72}{0.4} = 3.35.$$ $$a(x) = f''(x) \approx \frac{f(x+h) - 2f(x) + f(x-h)}{h^2}.$$ $$a(1.2) = f''(1.2) \approx \frac{f(1.4) - 2f(1.2) + f(1.0)}{0.2^2} = \frac{4.06 - 2 \cdot 3.32 + 2.72}{0.04} = 3.5.$$

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