1. The position of a particle is measured at certain instances of time as given below. Perform hand calculations to predict the velocity and acceleration at t = 0,1 and 2 seconds using the forward finite differencing scheme presented in class. [25+25 = 50 points]

Certain bacteria (such as aquaspirillum magnetotacticum) tend to swim toward the earth’s geographic north pole because they contain tiny particles, called magnetosomes, that are sensitive to a magnetic field. if a transmission line carrying 100 a is laid underwater, at what range of distances would the magnetic field from this line be great enough to interfere with the migration of these bacteria? (assume that a field less than 5% of the earth’s field would have little effect on the bacteria. take the earth’s field to be 5.0 * 10-5 t, and ignore the effects of the seawater.)