Answer:
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.
