# Error in acceleration

by bruno67
Tags: acceleration, error
 P: 32 Denote by $V(x)$ the speed of a particle at position x. Let's call $v(x;\zeta)$ a measurement of it, which depends on some parameter $\zeta$, and denote the error by $$\epsilon(x;\zeta)=v(x;\zeta)-V(x).$$ In order for the measurement to produce meaningful results, we must have some kind of error estimate such that, for any x $$|\epsilon(x;\zeta)|\le E(x;\zeta)$$ where E is a known positive function, which ideally tends to zero as $\zeta$ tends to zero (we are not considering quantum mechanical effects). My question is: can we obtain a similar estimate for the error in the derivative of $v(x;\zeta)$ (e.g., as a function of $E(x;\zeta)$, $V(x)$ or $V'(x)$) from the information given above, or do we not have enough information? You can assume that the derivative of $v(x;\zeta)$ is calculated by finite difference, and that the discretization error involved is negligible.