or as its research methodology, you could do something that doesn't require too much skill in either field, and make a battery discharger to log both constant current or constant power
in both cases the circuit to apply the load is very simple to make, and as for the actual discharge time, you can either be a little advanced and log the voltage vs time with say a micro's ADC, or simplify it and just set up a basic timer, so when battery voltage drops below "X" volts it stops the timer,
its also going to be something i doubt most students would do so you'll get a bit ahead of the group by doing something different,