the velocity-time graphs represent the motion of three different objects. identify any object that is getting faster or speeding up. tap on all that apply. tap to select or deselect graphs.

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# Answer: The first graph, the second graph, and the third graph (all three graphs) # Brief Explanations: 1. For the first graph: Velocity is positive and increasing (slope is positive), so speed (magnitude of velocity) is increasing (speeding up). 2. For the second graph: Velocity is negative and becoming more negative (slope is negative, velocity magnitude increasing), so speed is increasing (speeding up). 3. For the third graph: Velocity is negative and approaching zero (becoming less negative), but wait, no—wait, the third graph: velocity starts negative and moves towards zero? Wait, no, looking at the axes: velocity on y - axis, time on x - axis. The third graph: the line is from negative velocity towards zero? Wait, no, maybe I misread. Wait, no—speeding up means that the magnitude of velocity is increasing. So if velocity is negative and its magnitude is increasing (getting more negative) or velocity is positive and its magnitude is increasing (getting more positive). Wait, the third graph: let's re - examine. The third graph: the velocity starts at a negative value and moves towards zero? No, wait, the line is going from below the x - axis (negative velocity) towards the x - axis? Wait, no, maybe the third graph is a line that has a positive slope (since it's going from negative to less negative or towards positive? Wait, no, the slope: if the line is going from a negative velocity value towards zero (moving right along time), the slope is positive (since velocity is increasing from negative to zero, so the change in velocity over time is positive). But speed is the magnitude of velocity. So if velocity is negative and increasing (towards zero), the magnitude of velocity is decreasing. Wait, I made a mistake earlier. Let's correct: Speeding up occurs when the velocity and acceleration have the same sign (acceleration is the slope of the velocity - time graph). - First graph: Velocity is positive (above x - axis), slope (acceleration) is positive. So velocity and acceleration same sign → speeding up. - Second graph: Velocity is negative (below x - axis), slope (acceleration) is negative. So velocity and acceleration same sign → speeding up (since negative velocity becoming more negative, speed (|v|) is increasing). - Third graph: Velocity is negative (below x - axis), slope (acceleration) is positive (since the line is going from negative velocity towards zero, so velocity is increasing (becoming less negative)). So velocity is negative, acceleration is positive → opposite signs → slowing down. Wait, so my initial answer was wrong. Let's re - analyze: To determine speeding up: - Case 1: Velocity $ v>0 $ (positive direction) and acceleration $ a > 0 $ (velocity increasing in positive direction) → speed increases. - Case 2: Velocity $ v < 0 $ (negative direction) and acceleration $ a<0 $ (velocity becoming more negative, so speed (|v|) increases). First graph: $ v\geq0 $, $ a>0 $ (slope positive) → speeding up. Second graph: $ v\leq0 $, $ a < 0 $ (slope negative) → velocity becomes more negative, so speed (|v|) increases → speeding up. Third graph: $ v<0 $, $ a>0 $ (slope positive, since the line is going from negative v towards 0, so $ \Delta v/\Delta t>0 $) → velocity is negative, acceleration positive → opposite signs → speed (|v|) decreases (slowing down). So the correct answer is the first and second graphs. Wait, maybe the third graph is drawn differently. Let me re - look at the graphs: First graph: line from (0,0) going up (positive velocity, positive slope) → speeding up. Second graph: line from (0,0) going down (negative velocity, negative slope) → velocity becomes more negative, speed increases → speeding up. Third graph: line from below the x - axis (negative velocity) going up towards the x - axis (so velocity is increasing from negative to zero, then maybe positive? Wait, no, the graph: if it's a line that starts at negative velocity and has a positive slope, then acceleration is positive. So when velocity is negative and acceleration is positive, the object is slowing down (since it's moving in negative direction but accelerating in positive direction, so the speed (|v|) is decreasing as it approaches zero). When velocity becomes positive and acceleration is positive, then it's speeding up. But in the part of the graph shown (before velocity reaches zero), it's slowing down. So in the given graphs, the first and second are speeding up. So the correct answer is the first graph (velocity positive, increasing) and the second graph (velocity negative, becoming more negative, so speed increasing). The third graph: velocity negative, increasing towards zero (so speed decreasing), so not speeding up. So the answer should be the first and second graphs.

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