Good question. In this type of problem you already know a few variables, so you can figure out the rest using formulas. Let's see what we know (by the way, I"m assuming you already know what speed b is and how much time it takes to reach it from speed a. If you don't please let me know):
distance (d) = ? This is what you want to figure out.
Initial speed (Vi) = a (you already know this).
Final speed (Vf) = b (you already know this).
time taken to go from speed a to speed b = t (you already know this as well).
So the variables we know are: Vi, Vf, and t. The unknown variable is: d
There are a few formulas you can use to find d, but in both you need to know acceleration (a). To do this we use the formula:
vf = vi + at
Now you simply plug in what you know for vf, vi, t, and algebraically solve for a. Remember to include your units and then use them in your calculations (for example, vf would have the unit "steps/second"). 234
Treat the units as variables (like x in algebra), where you can add/subtract like terms.
After solving the above equation for a, you now know acceleration. Here you can choose between two formulas for solving for d (distance):
vf^2 = vi^2 + 2ad
or
d = vi * t + 0.5a * t^2
You can use either one of these formulas to solve for d. Just plug in what you know for the variables and then algebraically solve for d. In this case I would use the bottom formula, since d is already isolated by itself.
For the future, here are four kinematics formulas that you can use to solve most basic kinematics problems (three of them are ones I've already typed in this post):
vf = vi + at
v_average = (vf + vi) / 2 ......... v_average is just average speed
vf^2 = vi^2 + 2ad
d = vit + 0.5at^2
For these you can always rearrange the variables to solve for a specific unknown.
You could also go to Google Images and just type in "Kinematics formulas". You should find ones that are similar to what I listed. You can almost always rely on these.
If you have any questions on this, please let me know. 234