Answer
$a = 4.92\times 10^{-21}~m/s^2$
Work Step by Step
The gravitational force between the earth and the meteorite will cause both objects to accelerate toward each other. We can find the acceleration of the earth just before impact. Let $M_E$ be the mass of the earth. Then;
$F_G = M_E~a$
$\frac{G~M_E~M_M}{R^2} = M_E~a$
$a = \frac{G~M_M}{R^2}$
$a = \frac{(6.67\times 10^{-11}~m^3/kg~s^2)(3000~kg)}{(6.38\times 10^6~m)^2}$
$a = 4.92\times 10^{-21}~m/s^2$
