Which quantity can be negative depending on the chosen coordinate direction?

Which quantity can be negative depending on the chosen coordinate direction?

• A. Displacement
• B. Speed
• C. Distance
• D. Time

Answer: (D)

The thing being tested is how sign conventions affect numbers. When you set up a coordinate system, you pick a positive direction for that axis, and quantities that have direction can come out with a negative sign if they point the other way. Speed and distance are magnitudes, so they stay nonnegative. Displacement is a signed quantity along a chosen straight line, so it can be positive or negative depending on whether the motion goes with or against the positive direction. Time is usually treated as something that only increases, but time coordinates are just numbers in a chosen coordinate system. If you define the time axis to run opposite the usual forward-in-time direction, then time values can become negative for events that occur after the origin in the standard view. In that sense, time can be negative depending on how you set up the time origin and the direction of the time axis. This is why time can take negative values under a flipped convention, even though we commonly take it as positive in everyday problems.

The thing being tested is how sign conventions affect numbers. When you set up a coordinate system, you pick a positive direction for that axis, and quantities that have direction can come out with a negative sign if they point the other way. Speed and distance are magnitudes, so they stay nonnegative. Displacement is a signed quantity along a chosen straight line, so it can be positive or negative depending on whether the motion goes with or against the positive direction.

Time is usually treated as something that only increases, but time coordinates are just numbers in a chosen coordinate system. If you define the time axis to run opposite the usual forward-in-time direction, then time values can become negative for events that occur after the origin in the standard view. In that sense, time can be negative depending on how you set up the time origin and the direction of the time axis. This is why time can take negative values under a flipped convention, even though we commonly take it as positive in everyday problems.