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An object is moving with velocity given by where v­z(t) = 0. From this, one can conclude (a) that the acceleration (A) will have no components that are identically zero. (B) may have some componets that are identically zero. (C) will have only a z component that is identically zero. (D) will have an identically zero z component, and maybe an identically zero component in the x or y direction. (b) and that the position (A) will have no components that are identically zero. (B) May have some components that are identically zero. (C) Will have only a z component that is identically zero. (D) Will have an identically zero z component, and maybe. An identically zero component in the x or y direction.

An object is moving with velocity given by where v­z(t) = 0. From this, one can conclude           
(a) that the acceleration
(A) will have no components that are identically zero.
(B) may have some componets that are identically zero.
(C) will have only a z component that is identically zero.
(D) will have an identically zero z component, and maybe an identically zero component in the x or y direction.
(b) and that the position
(A) will have no components that are identically zero.
(B) May have some components that are identically zero.
(C) Will have only a z component that is identically zero.
(D) Will have an identically zero z component, and maybe. An identically zero component in the x or y direction.

 

Grade:upto college level

1 Answers

Deepak Patra
askIITians Faculty 471 Points
9 years ago
(a)
The correct option is: (D) will have an identically zero z component, and maybe an identically zero component in x or y direction.
(b)
The correct option is: (D) will have an identically zero z component, and maybe an identically zero component in x or y direction
(a)
The acceleration of the object with velocity vector\overrightarrow{v}(t) = v_{x}(t)\widehat{i} + v_{y}(t)\widehat{j} + v_{z}\widehat{k}
is:

233-1508_14.PNG
From this equation it is clear that the acceleration of the object depends on the change in magnitude of x component of velocity and y component of velocity respectively. Therefore the acceleration vector have an identically zero z component. Depending upon the values of vx (t) and vy (t), the x and y component of acceleration vector can also become zero.
However, if vx (t) and vy (t) are time dependent functions, x and y component of acceleration vector is guaranteed to be non-zero.
Therefore, the correct option is (D), and the rest are ruled out.
It is important to note that (C) comes closer to (D), but (C) rules out the probability that the acceleration vector can have zero x and y components.
(b)
It can be deduced from equations\overrightarrow{a}(t) = \frac{d}{dt} v_{x}(t)\widehat{i}+ \frac{d}{dt}v_{y}(t)\widehat{j} and \overrightarrow{v} (t) = v_{x} (t)\widehat{i}+v_{y}(t)\widehat{j} (v_{z}(t)= 0) that the object move in the xy the plane, and its motion is restricted in two dimensions. Therefore there will be no z component in the position vector of the object, however there will be components of position vector in x and y directions respectively.
The object can also have identically zero x and y components of position vector (if the objects move along the axis), but this would ensure that either vx (t) of or vy (t) to be zero.
Therefore, the correct option is (D), and the rest are ruled out

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