Answer
It takes around 79 days for the probe to reach the given velocity.
Work Step by Step
First, we are given $F=56mN = 5.6\times10^{-2}N$ and $m=474kg$
Following Newton's 2nd law equation, we can calculate the acceleration of the probe.
$$a=\frac{F}{m}=\frac{5.6\times10^{-2}}{474}=1.18\times10^{-4}m/s^{2}$$
Next, as we have $a=1.18\times10^{-4}m/s^2, v_0=0, v=805m/s$, we can calculate the time it takes to reach the given velocity, using kinematics equation for constant $a$ from Chapter 2:
$$v=v_0+at$$ $$t=\frac{v-v_0}{a}=\frac{v}{a}=\frac{805}{1.18\times10^{-4}}=682.2\times10^4s$$ $$t\approx79 days$$
