Determining initial velocity of cart before collision using position-time data

[toittoiger]

I am doing a Physics Lab where you have to measure initial and final velocities of two carts colliding in order to find the momentum. In this first category, you push a cart with a bumper into another cart with a bumper so that the first one completely stops right when it hits the second one. I am just wondering how you would calculate the initial velocity of the first cart I had to push off. Is the initial velocity right before it hits the cart or when it leaves my hand...etc. If you could please tell me what you think the initial velocity might be from this following data, that would be great. Here is the data:

t (s) d (m) ∆d (m) ∆t (s) v (m/s)
0 0
0.1 0.01 0.01 0.1 0.1
0.2 0.027 0.017 0.1 0.17
0.3 0.062 0.035 0.1 0.35
0.4 0.114 0.052 0.1 0.52
0.5 0.19 0.076 0.1 0.76
0.6 0.287 0.097 0.1 0.97
0.7 0.39 0.103 0.1 1.03
0.8 0.491 0.101 0.1 1.01
0.9 0.588 0.097 0.1 0.97
1 0.682 0.094 0.1 0.94
1.1 0.772 0.09 0.1 0.9
1.2 0.858 0.086 0.1 0.86
1.3 0.9431 0.0851 0.1 0.851
1.4 1.022 0.0789 0.1 0.789
1.5 1.097 0.075 0.1 0.75
1.6 1.16 0.063 0.1 0.63
1.7 1.227 0.067 0.1 0.67
1.8 1.244 0.017 0.1 0.17

 

[HallsofIvy]

Strictly speaking, the initial velocity is just as it leaves your hand which would be
Δ d/Δ t for the first two times in your data list. However, that's really assuming that velocity remains constant until the collision. You might want to consider (distance at collision- distance at start)/(time of collision- time of start) as a better approximation.