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29 April, 21:17

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.

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  1. 29 April, 21:33
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    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.
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