Question

which of the velocity vs. time graphs above represents an object that begins with a positive velocity, slows to a complete stop, then accelerates back to the original velocity?
just 4
5 and 6
just 3
1 and 4
2 and 3

Explanation:

To solve this, we analyze the velocity - time graph characteristics:

1. The object starts with positive velocity, so the graph starts above the time axis (v>0 initially).
2. It slows to a stop: this means the velocity decreases (slope is negative as acceleration is negative) until v = 0.
3. Then it accelerates back to original velocity: velocity increases (slope positive) back to the initial positive velocity value.

Now let's analyze each option:

• Option "just 4": Unlikely as we need two phases (deceleration to stop then acceleration) and maybe more than one graph.
• Option "5 and 6": If 5 and 6 have negative initial velocity (start below time axis) or don't follow the stop - accelerate back pattern, they are out.
• Option "just 3": One graph may not be enough, and likely 3 doesn't match the full pattern.
• Option "1 and 4": If 1 and 4 don't show the decelerate to stop then accelerate back, they are out.
• Option "2 and 3": Graphs 2 and 3 likely start with positive velocity, decelerate to 0 (slope negative), then accelerate back to original velocity (slope positive, reaching back to initial v).

Answer:

2 and 3