c. During a small time interval from just before instant 2 until just after instant 2, does the distance between cart A and cart B increase, decrease, or remain the same? decrease

Question

c.    During a small time interval from just before instant 2 until just after instant 2, does the distance between cart A and cart B increase, decrease, or remain the same? decrease

BlackTom AI · Accepted Answer

The question asks us to assess how the separation between cart A and cart B changes over a tiny interval around instant 2.
Option analysis:
- If the distance decreases: this means the relative motion of the carts is such that they are getting closer together during that brief window. In other words, the component of their relative velocity directed along the line joining the carts is negative, causing the separation to shrink as time advances through instant 2.
- If the distance remained the same: that would require the carts to have zero relative velocity along the line of centers during the interval, or for any approach to be exactly canceled by an opposing component. Absent evidence of such a perfect balance, this option is unlikely if the scenario involves motion through or past instant 2.
- If the distance increased: this would indicate the carts are moving apart during the interval, meaning the relative velocity along the line joining them is positive. This would contradict the given answer of decrease and would imply a different dynamical situation (e.g., they move away from each other at that moment).
- If there were multiple conflicting motions (e.g., one cart pausing while the other moves), the net effect on distance would still have to be evaluated by the sign of the rate of change of separation; without such details, assuming decrease requires that the dominant relative motion around instant 2 brings the carts closer.
In summary, the decrease in distance over a small interval around instant 2 corresponds to a negative rate of change of separation, i.e., the carts are approaching each other during that brief moment. This aligns with the provided answer indicating a decrease, whereas remaining the same or increasing would require different instantaneous velocities or timing that are not indicated here.

PHYS 114 B Tutorial Practice 1 - Acceleration in 1D

c. During a small time interval from just before instant 2 until just after instant 2, does the distance between cart A and cart B increase, decrease, or remain the same? decrease

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