a winch is probably your best bet. there are plenty that will lift in excess of what you are looking for. the benefit of a winch over just a dc motor is that it will typically be dc powered and already have a cable, guide, and proper gearing- all things you'd have to engineer on your own...
well i spent some time thinking about this before it occurred to me that this is a rather old post, and the semester is over so you probably already turned in a design. but I'm going to give my sentiment regardless because i am bored at work. i think that if you were deadset (or required) to use...
A particle moves along the x-axis according to the equation:
x = 1.92 + 3.09t − 1.00t2,
Where x is in meters and t is in seconds?
a) find the position of the particle at t=3.4s
-I get this part. (0.866m)...