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note: this is a multi-part question. once an answer is submitted, you will be unable to return to this part. a girl operates a radio-controlled model car in a vacant parking lot. the girl’s position is at the origin of the xy coordinate axes, and the surface of the parking lot lies in the x-y plane. she drives the car in a straight line so that the x coordinate is defined by the relation x(t)

Sagot :

At time t, the position is x(t) = 0.5t3 - 3t2 + 3t + 2.

What are coordinates?

  • Coordinates are two numbers (Cartesian coordinates) or a letter and a number that point to a specific point on a grid known as a coordinate plane.
  • A coordinate plane has four quadrants and two axes: x (horizontal) and y (vertical).

To find the position:

The derivative of x with respect to t is zero when the velocity is zero. That is to say,

  • x' = 1.5t² - 6t  + 3 = 0 or t² - 4t + 2 = 0

Use the quadratic formula to solve.

  • t = (1/2) [ 4 +/- √(16 - 8)] = 3.4142 or 0.5858 s

When t =0.5858 s, the position is:

  • x = 0.5(0.5858³) - 3(0.5858²) + 3(0.5858) + 2 = 2.828 m

When t=3.4142 s, the position is:

  • x = 0.5(3.4142³) - 3(3.4142²) + 3(3.4142) + 2 = -2.828 m

Reject the negative answer.

So, when t = 0.586 s, the velocity is zero and the distance is 2.83 m.

The second derivative of x with respect to t is zero when the acceleration is zero.

That is to say,

  • 3t - 6 = 0
  • t = 2

The distance traveled is:

  • x = 0.5(2³) - 3(2²) + 3(2) + 2 = 0

So, when the acceleration is zero, t = 2 s, and the distance traveled is zero.

Therefore, at time t, the position is x(t) = 0.5t3 - 3t2 + 3t + 2.

Know more about coordinates here:

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The correct question is given below:

A girl operates a radio-controlled model car in a vacant parking lot. the girl’s position is at the origin of the XY coordinate axes, and the surface of the parking lot lies in the XY plane. she drives the car in a straight line so that the x coordinate is defined by the relation x(t) = 0.5t3 - 3t2 + 3t + 2 where x and t are expressed in meters and seconds, respectively. determine when the velocity is 0 m/s, and the position and the total distance traveled when the acceleration is zero.

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