Question

When is the object moving to the right parametric equations

Answer 1

An object described by parametric equations is moving to the right if the x-component of its velocity vector is positive. The direction is determined by the sign of the x-component of the derivative of its position vector with respect to time.

Step-by-step explanation:

In mathematics, particularly in the study of parametric equations, an object is said to be moving to the right if its velocity in the x-direction is positive. When discussing parametric equations that describe motion, the velocity vector can be obtained by the derivative of the position vector with respect to time. If the x-component of this velocity vector is positive, then the object is moving to the right.

As an example, consider the parametric equation for an object's motion given by the vector function st = (4.0Î + 3.0Ĵ + 5.0k) m/s. The object is moving to the right if at time t the derivative of s with respect to t in the x-direction (represented by the Î component) is positive. In this case, since the x-component is 4.0 m/s, the object is indeed moving to the right.

To evaluate whether the object is moving to the right at different time intervals, one would need to observe the velocity or the derivative of the position function in the x-direction at those specific times. The sign of the x-component of velocity indicates the direction of motion: positive for to the right and negative for to the left.

Answer 2

That is, for a moving object whose parametric equations are known, the position function is a function that “takes in” a time t and “gives out” the position vector r(t) for the object's position at that time. and a(t) = v′(t) = r′′(t) = 〈x′′(t),y′′(t),z′′(t)〉 = x′′(t)i + y′′(t)j + z′′(t)k.

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