Take a long exposure photo of the
cart with a blinking LED to track the displacement of the cart
in equal time intervals for a level track or an inclined
track.
It's best to catch the cart before it hits the endstop.
NOTES
The Canon camera times out after a
minute or so of inactivity, but restarts with the last
settings preserved.
The LED has two blink rates: 100 Hz and 3 Hz, accessed
by pressing the power button two or three times.
Connect the camera to the AV system with its mini-USB - RCA
cable to show the live view and the resulting photo. Set
the shutter speed to the desired time (5 seconds in the above
photo) and adjust the aperture to underexpose the image a bit
so the light from the LED stands out.
For accelerated motion, a three-cm spacer (chalkboard eraser)
under one leg of the track is steep enough that frictional
losses are not obvious and shallow enough to get several data
points. In this case, a five-second exposure works well.