I am new to working out and the trainer set the machines up for me with what seems like the maximum range of motion and the machine times me so that I have to spend at least 1 second up and down -- and try to go slower than that because I thought you were supposed to . But I see people -- especially men -- doing very fast short up and down lifts with a narrow range of motion. What are they doing and why? Is this a legitimate alternative? ( not that I'm planning on trying it.)
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That's a downside of watching others in the gym because often they don't know what they're doing. Your trainer is correct in how you were shown how to do the lift.

With VERY few exceptions, if you're not doing the complete lift you're not doing the lift at all. I suspect these guys who aren't lifting all the way probably are lifting too much weight to have proper form and don't know what they're doing. At the least they aren't getting the full benifit of the exercise, at the most they're risking injury by not doing the exercise correctly.

Stick to the one second up one second down routine going all the way down and up and you'll do fine. You should also pause on the low part of the lift for added control.

Source(s):
www.bodybuilding.com