Answer:
A) The initial position of the particle is 2 meters.
B) The velocity of the particle at any time t is represented by .
C) The acceleration of the particle at any time t is represented by .
D) The velocity of the particle at the moment when is -2 meters per second.
Step-by-step explanation:
A) From statement we know that , where is the time, measured in seconds, and is the distance, measured in meters. The initial position of the particle is calculated by evaluating the function presented above at . That is:
The initial position of the particle is 2 meters.
B) According to the Theory on Kinematics, we see that velocity is the rate of change of position in time. In other words, we need to derive the equation once:
(1)
Where is the velocity, measured in meters per second.
The velocity of the particle at any time t is represented by .
C) And the acceleration is the rate of change of velocity in time. In other words, we need to derive the equation above:
(2)
The acceleration of the particle at any time t is represented by .
D) At first we solve the function position for , that is:
(3)
The only reasonable root of the polynomial is .
And now we evaluated the velocity function at given result:
The velocity of the particle at the moment when is -2 meters per second.