An object moves through in the horizontal xy plane with a position vector given by7 = (-bịt³ + b2t)î + (c1t² – c2t + c3)jAssume that b1, b2, c1, c2, and c3 are positive constants. Which of the followingstatements must be true? [There may be more than one correct answer]| The object's initial acceleration is zero| The object never changes direction.| The object is initially located at the origin.The object's initial velocity is directed in the 4th quadrant.As time passes, the object's acceleration is directed in the 2nd quadrant.

Position function: r→=-b1t3+b2ti^+c1t2-c2t+c3j^At t=0 ,Initial position of an obejct is as…

Answered: An object moves through in the…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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An object moves through in the horizontal xy plane with a position vector given by
7 = (-bịt³ + b2t)î + (c1t² – c2t + c3)j
Assume that b1, b2, c1, c2, and c3 are positive constants. Which of the following
statements must be true? [There may be more than one correct answer]
| The object's initial acceleration is zero
| The object never changes direction.
| The object is initially located at the origin.
The object's initial velocity is directed in the 4th quadrant.
As time passes, the object's acceleration is directed in the 2nd quadrant.

Expert Solution

Step 1

Position function:

$\vec{r} = (- b_{1} t^{3} + b_{2} t) \hat{i} + (c_{1} t^{2} - c_{2} t + c_{3}) \hat{j} A t t = 0, I n i t i a l p o s i t i o n o f a n o b e j c t i s a s f o l l o w s : \vec{r_{o}} = c_{3} \hat{j}$

Initially object is not located on the origin

Acceleration of an object:

$a = \frac{d^{2} \vec{r}}{d t^{2}} h e n c e, \vec{a} = \frac{d^{2} [(- b_{1} t^{3} + b_{2} t) \hat{i} + (c_{1} t^{2} - c_{2} t + c_{3}) \hat{j}]}{d t^{2}} \vec{a} = \frac{d}{d t} [(- 3 b_{1} t^{2} + b_{2}) \hat{i} + (2 c_{1} t - c_{2}) \hat{j}] \vec{a} = (- 6 b_{1} t) \hat{i} + (2 c_{1}) \hat{j} A t t = 0 I n i t i a l a c c e l e r a t i o n o f o b j e c t i s a s f o l l o w s : \vec{a_{o}} = 2 c_{1} \hat{j}$

From the acceleration function of an object, we can say that object

Initial acceleration of an object is not Zero
As the time passes, acceleration of an object is directed in second quadrant

As the time passes, Direction of r vector is changing.

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