Acceleration is defined as the rate of change of velocity over time. An acceleration of \(3.5 , \text{m/s}^2\) means that the velocity of the object increases by \(3.5 , \text{m/s}\) every second in the specified direction.
If we just have the magnitude of the acceleration (3.5 m/s²), it indicates the strength of the acceleration, but the sign (positive or negative) determines the direction.
To interpret your options:
- (a): "the object is traveling 3.5 m/s/s in a positive direction" – This suggests the acceleration is in a positive direction.
- (b): "the object is traveling 3.5 m/s/s in a negative direction" – This suggests the acceleration is in a negative direction.
- (c): "the object is traveling 3.5 m/s in a negative direction" – This incorrectly refers to speed, not acceleration.
- (d): "the object is traveling 3.5 m/s in a positive direction" – This also incorrectly refers to speed, not acceleration.
Given that acceleration doesn't refer to the current speed but to the rate of change of speed, the relevant answers are the first two, which provide context about the direction of acceleration.
Thus, if you know the context in which the acceleration is defined (positive or negative), you can determine the correct interpretation. Since the problem does not specify the direction of the acceleration, both options (a) and (b) could potentially be correct, but you can't definitively select one without that information.
In conclusion, an acceleration of \(3.5 , \text{m/s}^2\) indicates an increase in velocity at a rate of \(3.5 , \text{m/s}\) every second in the given direction (whether positive or negative, which is not specified in the question).
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