Physics help!! the problems are here...(Motion in straight line)?

[lisa rowe]

Here are three of first problems in this chapter. Please explain and show the work or equations so that I know how to get to the answer. Thank you, I greatly appreciate your time.
Know the answer for any or all??? by the way ^ means -t is an exponent at the top



1)An electron moving along the x-axis has a position given by x=16te^-t meters where t is in seconds. How far is the electron from the origin when it momentarily stops?



2)A rock is dropped from a 100 m high cliff. How long does it take to fall a) the first 50 m b)the second 50 m ???

3)The head of a rattlesnake can accelerate at 50 m/s² in striking a victim. If a car could do as well, how long would it take to reach a speed of 100 km/hr from rest????

[Steve]

1) v = (d/dt)(16(e^-t(1-t)).....For v = 0, t = 1. Putting t = 1 into the expression for x -> x = 16/e = 5.886 m.

2) t = ?(2y/g) -> t1 = 3.194 s and t2 = 4.517 - t50 = 1.323 s

3) t = v/a = (100/3.6)/50 = .555 sec