Too wide a question set, and some don't matter.
How fast?: 30 kph is getting fast for something small and unstable. Energy at 30 kph is \$(\dfrac{30}{20})^2\$ which is over double of that at 20 kph. Probability of pedestrian death in vehicle impact is \$\sim\sim\sim\sim\dfrac{V^2}{5000}\$ (V in kph). At 30 kph, the chance is \$\dfrac{30^2}{5000} = \sim 20%\$. That formula is for cars and pedestrians but gives you some indication. 20 kph is a safer target for playing an takes less than 1/3 of the windage power that 30 kph does ! - see below.
Battery is probably lead acid as available cheap per energy content or surplus. Low energy per mass and energy per size are tolerable.
Voltage probably 12V or 24V. One or two x 12V batteries. More is possible but gets bulky / annoying. 12V is good enough. 24V favoured by commercial designs as lower current so lower IR wiring losses.
12V or 24V DC motors in the hundreds of Watts range are available on the surplus market BUT are not usually cheap as they ar sought after by people who want to do similar to what you wish to do - vehicles, robots, ... .
Windage = power losses due to air drag.
- Empirical formula - power required to overcome windage for a compact one person vehicle is
$$ Windage \, power = \frac{V^3}{180} $$
Power in Watts. V in kilometres per hour. Examples:
- 160 kph gives 22,500 Watts
- 30 kph gives 150 Watts
- 20 kph gives 44 Watts.
This is simply a translation of the old motorcyclists adage
It takes 30 horsepower to ton for a well tucked in rider with leathers :-)
There are other ways of calculating this, but that is good enough in such an inexact area. For example:
$$Power = 0.5 \times air \, density \times frontal \, area \times drag \, coefficient \times velocity^2$$
The motorcycle formulae is as easy :-).
For something approximating a flat plate this gives
$$\sim\sim\sim\sim Power = A \times V^3 $$
A in \$m^2\$, V in \$m/s\$
Take off one V and you get Drag (Newtons) \$\sim\sim A \times V^2\$.
This works well enough for bowling balls, raindrops, skydivers, field mice and parachutes.
SO
ie you need a say 200 Watt motor at minimum to get something like your desired 30 km/h top speed on the flat. Using a 12V battery that's about 16 amps.
An eg 7Ah "brick" alarm system battery would wilt very quickly under that current. Notionally 7/16 hour = 26 minutes but really quite a bit less.
A say 30 Ah car battery will notionally give you approaching two hours at top speed. Somewhat less in practice.
Look at the many small electric scooters/bikes/xxx around and see what they use and what ranges and speeds they claim.
Uphill
$$Power = \dfrac{Newton \times metres}{second} \text{or} \sim \dfrac{kg \times m}{s} \times 10 $$
To ascent a slope at 100% efficiency you need
$$ \sim Power = \frac{Mass \times height \, change}{second} \times 10 Watts $$
Mass in kg, \$h\$ is increase in vertical height per second.
To lift you up the slope in addition to windage.
For example, at 30 kph ~= 8 m/s if you ascend a 1 in 20 slope (about 3 degrees) your vertical height change per second is ~= 8/20 = 0.4 ms.
If all up vehicle and rider weight is 100 kg, then
$$Power \, needed = M \times h/s \times 10 = 100 \times 0.4 \times 10 = 400 Watts$$
This dominates your windage losses on hills of this slope.
If you really want to make this 'kid proof' (I have more experience with 'student proof', that might be a slightly weaker test) you should limit the voltage AND CURRENT delivered by the power source, and select each and every component to withstand that current and that (reverse!) voltage.
100 mA @ 4.5V is probably enough. Use two LM317s (one for current limit, one for voltage limit) or even a vintage ua723 for the power.
That sensing diode might be a problem. Would the 1N5817 not do? Or maybe you can put a small resistor in series with that 1N5711 to limit the short-circuit current to somthing it can handle.
For the transistors I would take something more beefy, maybe BD139/140.
Best Answer
Yes, supply approximately 3 V. (If you were to use higher voltage, you might need additional current limitation to avoid burning out the motor.)
You can connect AAA in series to add up the voltages, for example using a battery holder like https://www.sparkfun.com/products/14219 with a built-in switch:
You can also move up to AA for longer running time. There are many variants of battery holders available.
You will need basic soldering skills and it doesn't hurt to buy a cheap multimeter. I'd say you're running minimal risks with so low voltages. A 9 V battery will sting if you put your tongue to the terminals but that's pretty much it. Oh, and most people burn themselves on a solder iron once before learning to show proper care. You might be able to wrap the stripped wire ends on the motor terminals to avoid the soldering.
Have fun! :-)