A jogger is exercising along a long, straight road that runs north-south. She starts out heading north. In what direction is she running at time t = 20 min?

Question

BlackTom AI · Accepted Answer

To determine the jogger’s direction at t = 20 min, we need to look at the velocity versus time graph and identify the sign of the velocity at that exact moment.

Option 1: north. This would be correct if the velocity v_x were positive (pointing in the north direction) at t = 20 min. However, the graph shows a sharp drop in velocity at t = 20 min, changing from a positive value to a negative value right at that point, so the velocity is not positive at t = 20 min. Therefore, this choice misreads the sign of the velocity near t = 20.

Option 2: south. The key to this option is recognizing the discontinuity at t = 20 min: immediately after t = 20, the velocity becomes negative (v_x < 0), indicating motion toward the south. Since the question asks for the direction exactly at t = 20 min, many textbook conventions take the instantaneous velocity at a discontinuity to be the value after the discontinuity for motion direction. In this graph, the velocity right at and just after t = 20 min is negative, corresponding to south.

Option 3: south and then north. This would imply the jogger changes direction within a small interval around t = 20 min, i.e., the velocity would switch signs more than once near t = 20. The provided graph shows a single abrupt change in velocity sign at t = 20, not a back-and-forth pattern, so this option describes a more complex motion than is present.

Option 4: north and then south. This would require the jogger to start moving north, reverse to south, all around t = 20 in a manner that would yield a positive velocity before 20 and a negative velocity after 20 with a defined reversal at or near t = 20. The graph does not show a reversal before 20; it shows a continuous positive velocity up to the moment of the discontinuity, then a jump to a negative value at t = 20, so this option mischaracterizes the motion history.

In summary, the velocity is positive (northward) up to t = 20 min, but at t = 20 min there is an abrupt change to a negative velocity (southward). Since the question asks for the direction at t = 20 min, the negative velocity indicates the jogger is running south at that instant. The correct interpretation aligns with the negative velocity after the discontinuity, which makes south the intended direction at t = 20 min.

SPHY001 Graded Quiz 1 (Unit 1 and Unit 2)- Requires Respondus LockDown Browser

A jogger is exercising along a long, straight road that runs north-south. She starts out heading north. In what direction is she running at time t = 20 min?

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