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Using derivatives, it is found that:
i)
ii) 9 m/s.
iii)
iv) 6 m/s².
v) 1 second.
<h3>What is the role of derivatives in the relation between acceleration, velocity and position?</h3>- The velocity is the derivative of the position.
- The acceleration is the derivative of the velocity.
In this problem, the position is:
item i:
Velocity is the <u>derivative of the position</u>, hence:
Item ii:
The speed is of 9 m/s.
Item iii:
Derivative of the velocity, hence:
Item iv:
The acceleration is of 6 m/s².
Item v:
t for which a(t) = 0, hence:
Hence 1 second.
You can learn more about derivatives at brainly.com/question/14800626
Remember that the area of a rectangle is the length of the rectangle multiplied by the width of the rectangle.
In this case, we could say (where is the area of the rectangle):
Substituting the values the problem gave us for and
, we can find the formula for
in terms of
, which is:
The formula for the area of the rectangle would be A(x) = 10x³ - 20x² + 65x.