Finding acceleration due to gravity on a graph...?

I take it you mean the gradient =1/2 = g.That would be OK but it's not g on this planet,on earth g =10(pretty nearly) so what you have is not g but is a(for acceleration) in the system you measured.As for long times and in free fall on earth acceleration would eventually become zero because air resistance would eventually be equal to the downward force gm.RETHINK If you mean the slope is g/2 = 5m per sec per sec then this would be a reasonable result for an experiment where a m of 1 unit was falling under gravity while pulling a trolley of m 1 unit on a flat bed;Sounds like Fletcher's Trolley experiment to me.Just the same, in air a falling body would reach a fixed velocity(no more acceleration)when air resistance = downward force.Without air resistance or any other resistance there is NO limit to velocity in Newtonian Physics.