Timings on different slopes, 46.2 cm distance.

Rise measured for 44 cm run.

Timing of cart, 2.04 cm rise. Looks like 2.2 s – 3.7 s, or 1.5 s time interval. Implies about 40 cm/s^2 accel on slope about .04. Consistent if almost no friction.

My ‘one-two-three’ count?

Another trial on 2.04 cm

Looks more like 1.4 sec.

Now for 1.69 cm rise:

Looks like about 1.6 sec, accel around 32 cm/s^2. Change of 8 cm/2^s for slope change of about .007.

Another run at 1.69 cm rise:

Again about 1.6 sec.

Now with rise .95 cm:

Looks like about 2.8 sec. Implies accel around 8 cm/s^2.

Another on same slope:

Measuring `dt to within 1% we get accel vs. slope pairs:

{[0.02159090909, 11.45606030], [0.03840909090, 33.93939393], [0.04636363636, 43.94768133]}

Best-fit straight line is y = 1315.511308·x - 16.8598102.

Plots with assumed .1 sec and .2 sec anticipation:

Accelerations are 1316 cm/s^2, 1127 cm/s^2, 973 cm/s^2.

Conclusion: I probably anticipated by .2 sec. Repeat experiment with actual sounds.