a person pushing a stroller starts from rest, uniformly accelerating at a rate of 0.500 m/s2. What is the velocity of the stroller after it has traveled 4.75 m ?

[tex]v[/tex] is the final velocity of the object,
[tex]u[/tex] is the initial velocity of the object,
[tex]a[/tex] is the acceleration of the object, and
[tex]x[/tex] is the distance that the object had traveled while its velocity changed from [tex]u[/tex] to [tex]v[/tex].

Note that unlike other SUVAT equations, this one does not ask for the time required for the speed of the object to change from [tex]u[/tex] to [tex]v[/tex]. Since in this problem, time isn't given, this time-less equation would particular useful.

Here

[tex]v[/tex] the final velocity needs to be found.
[tex]u = 0[/tex] for the stroller started from rest.
[tex]a =\rm 0.500 \;m \cdot s^{-2}[/tex] is the acceleration of the stroller, and
[tex]x = \rm 4.75\; m[/tex] is the distance that the stroller traveled while its velocity changed from [tex]u[/tex] to [tex]v[/tex].

Rearrange the equation to isolate the unknown, [tex]v[/tex]:

[tex]v^{2} = u^{2} + 2 \; a \cdot x[/tex].

Make sure that all units are standard, so that the unit of the output will also be standard. Apply the equation:

[tex]v = \sqrt{u^{2} + 2 \; a \cdot x} = \sqrt{0^2 + 2 \times 0.500 \times 4.75 }\approx \rm 2.18\; m\cdot s^{-1}[/tex].

Hence the final velocity will be approximately [tex]\rm 2.18 m\cdot s^{-1}[/tex].