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An object moves in the xy plane with an acceleration that has a positive x component. At time t = 0 the object has a velocity given by (a) What can be concluded about the y component of the ac- celebration? (A) The y component must be positive and constant. (B) The y component must be negative and constant (C) The y component must be zero. (D) Nothing at all can be concluded about the y component. (b) What can be concluded about the y component of the velocity? (A) The y component must be increasing. (B) The)' component must be constant. (C) The)' component must be decreasing. (D) Nothing at all can be concluded about the variation of the)' component. (c) What can be concluded about magnitude of the velocity? (A) The magnitude of the velocity must be increasing. (B) The magnitude of the velocity must be constant. (C) The magnitude of the velocity component must be de- creasing. (D) Nothing at all can be concluded about the magnitude of the velocity.

An object moves in the xy plane with an acceleration that has a positive x component. At time t = 0 the object has a velocity given by 
(a) What can be concluded about the y component of the ac- celebration?
(A) The y component must be positive and constant.
 (B) The y component must be negative and constant
 (C) The y component must be zero.
 (D) Nothing at all can be concluded about the y component.
 (b) What can be concluded about the y component of the velocity?
(A) The y component must be increasing.
(B) The)' component must be constant.
(C) The)' component must be decreasing.
(D) Nothing at all can be concluded about the variation of the)' component.
(c) What can be concluded about magnitude of the velocity?
(A) The magnitude of the velocity must be increasing.
(B) The magnitude of the velocity must be constant.
(C) The magnitude of the velocity component must be de- creasing.
(D) Nothing at all can be concluded about the magnitude of the velocity.

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
7 years ago
(1)
The correct option is: (D) Nothing at all can be concluded about the component.
(2)
The correct option is:(D) Nothing at all can be concluded about the variation of component.
(3)
The correct option is:(D) Nothing at all can be concluded about the magnitude of velocity.
(1)
The question only states that the y component of acceleration is a positive constant and nothing about the y component. Therefore one cannot assume that the y component of acceleration is zero.
Therefore, (D) is the correct option and the rest are ruled out.
(2)
Without any idea about the nature of y component of acceleration (positive or negative and constant or variable), one cannot conclude anything about the y component of velocity at t ≠ 0.
Therefore, (D) is the correct option and the rest are ruled out.
(3)
The magnitude of velocity at any time is given as:
236-895_90.PNG
Here vx is the x component of velocity whereas vy is the y component of velocity at that time.
From part (a), one can conclude that the nature of y component of acceleration cannot be determined. Therefore one cannot know if the acceleration would increase or decrease the magnitude of y component of velocity at other times. Also, from equation|\overrightarrow{v}| = \sqrt{v_{x}^{2}+_{y}^{2}} , the dependence of magnitude on y component of velocity can clearly be seen .
Therefore, one cannot conclude anything about the magnitude of velocity and the correct option is (D), and the rest are ruled out.

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