Just done crash cart experiment with ticker tape.

Question reads, "Assuming that the acceleration is constant, then so long as we use the same time interval in each case, displacement will be proportional to acceleration. Explain why we can say that displacement is proportional to acceleration in this experiment".

Thanks :)

This sounds like one of those problems in which semantics plays a big part.

The equation for displacement with time (initial velocity = 0) is:

D = 0.5 AT^2

This indicates that displacement is proportional to the acceleration if time is a constant. But time isn't a constant. It increases. The displacement is also proportional to the square of elapsed time. So, I'm not even sure that we can say that displacement is proportional to acceleration. Maybe it has something to do with the particular experiment that you're doing. If you could, somehow, say that time was a constant, then you'd have the traditional formula

D = mA

And displacement would be proportional to acceleration. But that seems weird to me.