The position vector of particle moving in the xy-plane is .What is the distance traveled by the particle from to ? Round your answer to three decimal places.
A)9.870
B)10.354
C)12.335
D)42.912

Question

​The position vector of particle moving in the xy-plane is  .What is the distance traveled by the particle from  to  ? Round your answer to three decimal places. ​
A)​9.870 
B)​10.354 
C)​12.335 
D)​42.912

Quizplus · Accepted Answer

To find the distance traveled by the particle, we need to find the magnitude of the displacement between the initial and final positions.

Let the initial position vector be A and the final position vector be B.

A = 11eac44f_ebbb_1bee_bedf_450837860c05_TB7497_11 
B = 11eac44f_ebbb_1bef_bedf_315dc59f0774_TB7497_11

The displacement vector, AB = B - A

AB = (11eac44f_ebbb_1bef_bedf_315dc59f0774_TB7497_11) - (11eac44f_ebbb_1bee_bedf_450837860c05_TB7497_11)
 
AB = 11eac44f_ebbb_1bef_bedf_315dc59f0774_TB7497_11 - 11eac44f_ebbb_1bee_bedf_450837860c05_TB7497_11

AB = 190948fb10_TB7497_11

The magnitude of AB can be found using the distance formula:

|AB| = sqrt((x2 - x1)^2 + (y2 - y1)^2)

|AB| = sqrt((190948fb10_TB7497_11)^2)

|AB| = 10.354

Therefore, the distance traveled by the particle is 10.354 units.

​The Position Vector of Particle Moving in the Xy-Plane Is

The Position Vector of Particle Moving in the Xy-Plane Is