If a particle moves descibing a uniformly accelerated rectilinear motion, then, the distance that the particle travels Δx is related to the acceleration of the particle a, its initial speed v_0 and the time that it has traveled t, through the following equation:
[tex]\Delta x=v_0t+\frac{1}{2}at^2[/tex]Since the car is initially at rest, then v_0=0:
[tex]\begin{gathered} \Delta x=0\cdot t+\frac{1}{2}at^2 \\ \Rightarrow\Delta x=\frac{1}{2}at^2 \end{gathered}[/tex]Replace a=9m/s^2 and t=5.1s to find how far did the car travel during that time:
[tex]\Delta x=\frac{1}{2}(9\frac{m}{s^2})(5.1s)^2=117.045m\approx117m[/tex]Therefore, the car traveled a distance of 117 meters.
