A particle moves according to a law of motion s fstd, t > 0, where t is measured in seconds and s in feet. (a) Find the velocity at time t. (b) What is the velocity after 1 second? (c) When is the particle at rest? (d) When is the particle moving in the positive direction? (e) Find the total distance traveled during the first 6 seconds. (f) Draw a diagram like Figure 2 to illustrate the motion of the particle. (g) Find the acceleration at time t and after 1 second. (h) Graph the position, velocity, and acceleration functions for 0 < t < 6. (i) When is the particle speeding up? When is it slowing down? fstd t 2 e2t

Dimensional Analysis Dimensional analysis is a convenient way to convert quantities from one unit to another. It would be used in an instance where two volumes need to be added, but they are in different units. Dimensional analysis would help to put them in the same unit, so that they can then be added. It is like how fractions cannot be added when they have different denominators, so in order to add them a common denominator needs to first be found. Dimensional analysis could also be used to solve more complex problems such as determining the density (in g/cm )of a solid when only the diameter (in nm) of each atom and its mass (in amu) is known ahead of time. Above is the what and why, n ere is ow: Question: