Question

The position ) f (x of a particle moving in a line at various times k
x is given in the
following table. Estimate the velocity and acceleration of the particle at x = 2.1 .

x 1.0 1.2 1.4 1.6 1.8 2.0 2.2
f (x) 2.72 3.32 4.06 4.96 6.05 7.39 9.02

Answer 1

Answer on Question #46688 – Math – Algorithms | Quantitative Methods

The position $f(x)$ of a particle moving in a line at various times $k$

$x$ is given in the following table. Estimate the velocity and acceleration of the particle at $x = 2.1$.

x 1.0 1.2 1.4 1.6 1.8 2.0 2.2

f (x) 2.72 3.32 4.06 4.96 6.05 7.39 9.02

Solution.

Velocity at $x = 2.1$: $v(2.1) = \frac{f(2.2) - f(2.0)}{2.2 - 2.0} = \frac{9.02 - 7.39}{0.2} = 8.15$.

Velocity at $x = 2.2$: $v(2.1) = \frac{f(2.2) - f(2.0)}{2.2 - 2.0} = \frac{9.02 - 7.39}{0.2} = 8.15$.

Velocity at $x = 2.0$: $v(2.0) = \frac{f(2.0) - f(1.8)}{2.0 - 1.8} = \frac{7.39 - 6.05}{0.2} = 6.70$.

Acceleration at $x = 2.1$: $a(2.1) = \frac{v(2.2) - v(2.0)}{2.2 - 2.0} = \frac{8.15 - 6.70}{0.2} = 9.00$.

www.AssignmentExpert.com