The position vector describes the path of an object moving in space.Find the speed of the object.
B)
C)
D)

Question

The position vector  describes the path of an object moving in space.Find the speed  of the object. ​
B) ​ 
C) ​ 
D) ​

Quizplus · Accepted Answer

The speed of an object moving in space is given by the magnitude of its velocity vector. However, since only the position vector is provided in this question, we cannot directly determine the velocity vector and hence the speed.

Therefore, we need to make some assumptions or use additional information. One common assumption is that the object moves with constant speed along its path, in which case we can find the magnitude of its average velocity vector between any two points on the path.

Using this assumption, we can pick two arbitrary but convenient points on the path, say the initial and final positions. Let the initial position vector be:

r1 = 11eac44f_ebbe_7779_bedf_b75c70869f36_TB7497_11

and let the final position vector be:

r2 = 11eac44f_ebbe_2cad_bedf_dfeaa0672eb7_TB7497_11

To find the average velocity vector between these two points, we can subtract the initial from the final position vector and divide by the time taken to travel from r1 to r2. However, the time is not given in the question, so we need to find it from the position vectors.

One way to do this is to use the fact that the object moves with constant speed, so the distance traveled between r1 and r2 is equal to the speed multiplied by the time taken. Therefore, we can use the magnitudes of the position vectors to find the distance:

|Δr| = |r2 - r1| = 11eac44f_ebbe_b22d_bedf_44e483bd0831_TB7497_11

where Δr is the displacement vector between r1 and r2.

Since the speed is constant, we have:

|Δr| = speed × Δt

where Δt is the time taken to travel from r1 to r2.

Solving for Δt, we get:

Δt = |Δr| / speed = (11eac44f_ebbe_b22d_bedf_44e483bd0831_TB7497_11) / speed

Now we can find the average velocity vector:

vavg = (r2 - r1) / Δt

Substituting the given position vectors and the expression for Δt, we get:

vavg = [(11eac44f_ebbe_2cad_bedf_dfeaa0672eb7_TB7497_11) - (11eac44f_ebbe_7779_bedf_b75c70869f36_TB7497_11)] / [(11eac44f_ebbe_b22d_bedf_44e483bd0831_TB7497_11) / speed]

Simplifying the numerator, we get:

vavg = 11eac44f_ebbe_551e_bedf_b3087b40d2df_TB7497_11

Multiplying both sides by speed, we get:

speed = |vavg| × 11eac44f_ebbe_b22d_bedf_44e483bd0831_TB7497_11

Substituting the values, we get:

speed = 11eac44f_ebbe_c59d_bedf_c9e49b0016b7_TB7497_11

Therefore, the answer is C.

The Position Vector Describes the Path of an Object