Dynamics engineering problem

I have been out of the country for 2 years and am trying to remember all my calculus and engineering courses. I need a little help remembering how to solve the attached problem. (See attached file for full problem description)

Dynamics problem

A car starts from rest and moves along a straight line with an acceleration of a = (3s^(-1/3)) m/s^2, where s is in meters. Determine the car's acceleration when t = 4s.

The problem requires calculation of pressure on the bottom of a barge.

1) A loaded flat bottom barge floats in fresh water. The bottom of the barge is 4.06m below the water line. When the barge is empty the barge's bottom is only 1.36m below the water line. What is the difference between the pressure on the bottom of the loaded barge and the pressure at the water line? Answer in Pascals. 2) If the surface area of the bottom of the barge is 580m^2 what is the weight of the load in the barge? Answer in Newtons

Simple Harmonic Motion and waves: Velocity and acceleration

Please help with 14, 15 and 16 with step by step solutions showing equations used and answers. answer 14 not 16.1cm, answer 15 not 8.123 m/s, answer 16 not 19.6 m/s^2. (See attached file for full problem description)

The rotation matrix

(See attached file for full problem description) --- The rotation matrix [R], associated with a positive (in a right-hand sense) rotation α about the z-axis is: cosα sinα 0 -sinα cosα 0 0 0 1 • Derive the rotation Matrix [Q] relating (x, y, z) to a system (x', y', z') which is described by three consecutive Euler rotations about z, then y then x. • Show that [Q] is orthogonal. • The transformation rule for the strain tensor under a rotation is [ε'] = [Q] [ε ] [Q]T . Why is not possible to find a matrix [A] such that [ε '] = [A] [ε]? Write down three quantities that you know to be invariant under the rotation. • Wr... click for more