A block connected to a horizontal spring is in simple harmonic motion on a level, frictionless surface, oscillating with amplitude A around x = 0. Identify whether each of the following statements is true or false:

(a) If x = ±A then |v|=|vmax| and |a|=|amax|.
(b) If x = 0 then |v|=|vmax| and |a|= 0.
(c) If v > 0 then a < 0.
(d) If x > 0 then a < 0.
(e) If x > 0 then v > 0.

(a) assume the equation x = at^3 + bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. determine the dimensions of the constants a and b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.) (b) determine the dimensions of the derivative dx/dt = 3at^2 + b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.)

Give an example of a collision in real life. use the law of conservation of energy to describe the transfer of momentum. be sure and discuss the momentum before and after the collision occurs. you will need at least 3 sentences to thoroughly answer this question.

Asmall grinding wheel has a moment of inertia of 4.0×10−5 kg⋅m2 . what net torque must be applied to the wheel for its angular acceleration to be 150 rad/s2 ?