Train: we're given the initial velocity [tex]v_0[/tex] of 22.4 m/s, told that acceleration [tex]a[/tex] is a constant 3.5 m/s^2, and that it eventually stops so that its final velocity [tex]v[/tex] is 0 m/s. The total distance [tex]x[/tex] can then be computed by solving
[tex]v^2-{v_0}^2=2ax\implies\left(0\,\dfrac{\mathrm m}{\mathrm s}\right)^2-\left(22.4\,\dfrac{\mathrm m}{\mathrm s}\right)^2=2\left(-3.5\,\dfrac{\mathrm m}{\mathrm s^2}\right)x[/tex]
[tex]\implies x=71.6\,\mathrm m[/tex]
Cyclist: it starts at rest, so [tex]v_0[/tex] is 0 m/s, then it accelerate at a cosntant 3.2 m/s^2, and we're told it does so for 2.4 s. We can solve for [tex]v[/tex] via
[tex]v=v_0+at\implies v=\left(3.2\,\dfrac{\mathrm m}{\mathrm s^2}\right)(2.4\,\mathrm s)[/tex]
[tex]\implies v=7.7\,\dfrac{\mathrm m}{\mathrm s}[/tex]
Object: the answer they're looking for here is probably the first choice. But technically any one of these equation can be used to determine the total displacement [tex]x-x_0[/tex]. In order to properly use the other three you need to know the value of [tex]a_x[/tex] which can be computed with the given information, since constant acceleration means average/instantaneous accelerations are the same.
