Ablock of mass m is attached to a spring whose spring constantis k. the other end of the spring isfixed so that when the spring is unstretched, the mass is locate. assume that the +x direction is to the right.
the mass is now pulled to the right a distance a beyond the equilibrium position and released, at time t=0, with zero initial velocity.

assume that the vertical forces acting on the block balance eachother and that the tension of the spring is, in effect, the onlyforce affecting the motion of the block. therefore, the system willundergo simple harmonic motion. for such a system, theequation of motion is

a(t)=-\frac{k}{m}x(t),

(a) at what time t_1 does the block come back to its originalequilibrium position (x=0) for the first time?
express your answer in terms of someor all of the variables: a, k, and m.

(b) find the velocity v of the block as a function of time.
express your answer in terms of someor all of the variables: k, m, a, and t.

(c) find the acceleration a of the block as a function of time.
express your answer in terms of someof all of the variables: k, m, a, and t.

(d) specify when the magnitude of the acceleration of the blockreaches its maximum value. consider the following options:
only once during one period of motion,
when the block's speed is zero,
when the block is in the equilibrium position,
when the block's displacement equals either a or -a,
when the block's speed is at a maximum.
(e) find the kinetic energy k of the block as a function of time.
express your answer in terms of someor all of the variables: k, m, a, and t.

(f) find k_max, the maximum kinetic energy ofthe block.
express your answer in terms of someor all of the variables: k, m, and a.

(g) the kinetic energy of the block reaches its maximum when whichof the following occurs?

thedisplacement of the block is zero.
thedisplacement of the block is a.
theacceleration of the block is at a maximum.
the velocityof the block is zero.

State one advantage and one disadvantage of using a plane mirrior as a driving mirrior

Need asap which of these is an example of a hypothesis? (2 points) a. adults were not interviewed b. the investigation was time consuming c. the source of information was biased d. very few teenagers were interviewed scientists in different parts of the world have conducted experiments to find the speed of light in vacuum. if the results of the experiments are identical, they would most likely be (2 points) a.valid b. biased c. unreliable d. non-observable which of these questions can be answered using science? (2 points) a. what is the best career? b. does water exist on venus? c. should the use of automobiles be stopped? d. which is the most interesting subject to study? the models can be best used to (2 points) recreate something which is easily observed in nature prove that all atomic theories have the same meaning demonstrate the transformation of atomic theory into law represent the locations of subatomic particles in different atomic theories 22. (bws.06) scientists earlier believed that the lowest measurable temperature is the freezing point of ice. however, modern scientists believe that temperatures below the freezing point of ice can also exist. what best accounts for these different opinions? (2 points) scientists propose contradictory ideas to include all possibilities scientists come up with different hypotheses without enough evidence scientists propose different ideas to avoid repetition of scientific knowledge scientists having different interests may interpret the same data in different ways based on the graph, what is the most likely mass of an apple chosen randomly from the basket? (2 points) between 0.10 kg and 0.12 kg between 0.12 kg and 0.14 kg between 0.14 kg and 0.16 kg between 0.16 kg and 0.18 kg a scientist studies a model of a widely accepted theory about the position of planets and sun. the model would most likely the scientist to (2 points) prove that the theory would not change in the future demonstrate how the theory can be changed into a law understand facts which cannot be easily observed prove that all other facts about the universe are incorrect one scientist discovered a new theory on the evolution of the universe. what is the next step for the scientist to take? (2 points) transform the results of the theory into universal laws of nature inform the scientific community so they can verify the results call a press conference to make the discovery popular among people encourage scientists worldwide to find an appropriate application for the results the students' observations are listed below. when an iron nail is taken near the north pole (n) of the bar magnet, it is pulled towards the magnet. when an iron nail is taken near the south pole (s) of the bar magnet, it is pulled towards the magnet. the experiment was repeated by several students using different bar magnets. based on the investigations, which of these theories would the students most likely propose? (2 points) magnets attract iron nails the poles of a magnet attract all materials iron nails are attracted towards all materials iron nails have the same properties as magnets

Two technicians are discussing a starter that clicks repeatedly when the key is turned to the crank position. technician a says the solenoid hold-in winding is open. technician b says the solenoid pull-in winding is open. who is correct?