Which of the following combinations of position (x) and direction of motion would give a velocity in the x-direction that has a negative value? a. Positive x, moving towards the origin. b. Negative x, moving away from the origin. c. Both a and b. d. Positive x, moving away from the origin. e. Negative x, moving towards the origin.

c) Both a) and b) are the combinations that have a negative velocity.

Explanation:

The velocity is given by this equation:

v = Δx / Δt

Where

Δx = final position - initial position

Δt = elapsed time

Now let's evaluate the options. We have to find those combinations in which Δx < 0 since Δt is always positive.

a) If the initial position, x, is positive and you move towards the origin, the final position will be a smaller value than x. Then:

final position < initial position

final position - initial position < 0 The velocity will be negative.

b) If x is negative and you move away from the origin, the final position will be a more negative number than x. Again:

final position < initial position

final position - initial position < 0 The velocity will be negative.

Let's do an example to show it:

initial position = - 5

final position = - 10 (since you moved away from the origin)

final position - initial position = - 10 - (-5) = - 5

d) If x is positive and you move away from the origin, the final position will be a greater value than the initial position. Then:

final position > initial position

final position - initial position > 0 The velocity will be positive.

e) If x is negative and you move towards the origin, the final position will be a greater value than the initial position. Then:

final position > initial position

final position - initial position > 0 The velocity will be positive.

Let's do an example:

initial position = - 10

final position = - 5

final postion - initial position = - 5 - (-10) = 5

or with final position = 0

final postion - initial position = 0 - (-10) = 10

And so on.

The right answer is c) Both a) and b) are the combinations that have a negative velocity.