Question

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.

Explanation:

Step1: Analyze the first graph

The first graph has velocity starting at 0 and going negative (below the time axis) with increasing magnitude (steeper negative slope? Wait, no, the line is going down from 0, so velocity is negative and becoming more negative (speed is magnitude of velocity, so if velocity is -5 and becomes -10, speed is 5 then 10, so speeding up). Wait, no, let's recall: speeding up is when the magnitude of velocity is increasing, regardless of direction. So if velocity is negative and becoming more negative (more negative means larger magnitude), or positive and becoming more positive.

First graph: velocity starts at 0, goes negative (downward from 0 on velocity axis). So velocity is negative, and the slope (acceleration) is negative (since line is decreasing). So velocity and acceleration have the same sign (both negative), so the object is speeding up (because when velocity and acceleration have the same sign, speed increases). Wait, but let's check the second graph.

Second graph: velocity is negative (below 0 on velocity axis) and the line is going up (towards 0). So velocity is negative, acceleration is positive (since slope is positive). So velocity and acceleration have opposite signs, so speed is decreasing (since speed is |velocity|, if velocity is -3 and becomes -2, speed decreases from 3 to 2). So second graph: slowing down.

Third graph: velocity starts at 0, goes positive (upward from 0) and the line is increasing (positive slope, positive acceleration). So velocity and acceleration have the same sign (both positive), so speed is increasing (speeding up).

Wait, maybe I messed up the first graph. Let's re-express:

Velocity-time graph:

- First graph: velocity (y-axis) vs time (x-axis). The line starts at (0,0) and goes down (negative velocity) with a constant slope (constant acceleration, negative). So velocity is negative, acceleration is negative (same sign as velocity). So when velocity and acceleration have the same sign, the object is speeding up (because acceleration is in the same direction as velocity, so speed increases). For example, if velocity is -2 m/s (moving left) and acceleration is -1 m/s² (also left), then the speed (2 m/s) becomes 3 m/s, so speeding up.

- Second graph: velocity is negative (below 0) and the line is going up (towards 0). So velocity is negative, acceleration is positive (slope is positive). So velocity and acceleration have opposite signs. So speed is decreasing (e.g., velocity -3 m/s, acceleration +1 m/s²: velocity becomes -2, speed from 3 to 2, slowing down).

- Third graph: velocity is positive (above 0) and line is going up (positive slope, positive acceleration). Same sign, so speed increases (speeding up).

Wait, but maybe the first graph: if velocity is going from 0 to negative, is it speeding up? Let's think about speed: speed is the magnitude of velocity. At t=0, speed is 0. As time increases, velocity becomes more negative (e.g., -1, -2, -3...), so speed is 1, 2, 3..., so speed is increasing. So first graph: speeding up. Third graph: velocity goes from 0 to positive, increasing (1,2,3...), speed increasing. Second graph: velocity is negative, going towards 0 (e.g., -3, -2, -1...), speed decreasing (3,2,1...), so slowing down.

Wait, but maybe the first graph: when velocity is negative and becoming more negative, speed increases. Third graph: velocity positive and becoming more positive, speed increases. Second graph: velocity negative and becoming less negative (towards zero), speed decreases. So the objects speeding up are the first and third graphs? Wait, but the problem shows three graphs:

First graph: velocity (y) vs time (x), line from (0,0) downwards (negative velocity, increasing magnitude, so speeding up).

Second graph: velocity (y) is negative (below 0), line going upwards (towards 0), so velocity magnitude decreasing (slowing down).

Third graph: velocity (y) starts at 0, goes upwards (positive velocity, increasing magnitude, speeding up).

Wait, but maybe the first graph: if velocity is negative, and acceleration is negative (same direction as velocity), then speed increases. Third graph: velocity positive, acceleration positive, speed increases. So both first and third? But maybe the first graph: when velocity is negative, and it's moving away from zero (more negative), speed increases. Third graph: moving away from zero in positive direction, speed increases. Second graph: moving towards zero (less negative), speed decreases.

But maybe the question's graphs: let's re-express the three graphs:

1. Graph 1: Velocity starts at 0, goes negative (down) with constant slope (negative acceleration). So velocity and acceleration same sign (both negative) → speeding up.

2. Graph 2: Velocity is negative (below 0), goes up (towards 0) with constant slope (positive acceleration). Velocity and acceleration opposite signs → slowing down.

3. Graph 3: Velocity starts at 0, goes positive (up) with constant slope (positive acceleration). Velocity and acceleration same sign (both positive) → speeding up.

So the objects speeding up are Graph 1 and Graph 3? Wait, but maybe the first graph: when velocity is negative, and it's accelerating in the negative direction, so speed increases. Third graph: accelerating in positive direction, velocity positive, speed increases. So both. But maybe the problem's options: let's check the graphs again.

Wait, the user's image: three graphs. Let's describe each:

- First graph: velocity (y-axis) vs time (x-axis). The line starts at (0,0) and goes downward (negative velocity) with a constant slope (so acceleration is negative, constant). So velocity is negative, acceleration is negative (same direction as velocity), so speed (magnitude of velocity) increases. So this object is speeding up.

- Second graph: velocity (y-axis) is negative (below the zero line) and the line goes upward (towards zero) with a constant slope (so acceleration is positive, constant). Velocity is negative, acceleration is positive (opposite direction), so speed (magnitude of velocity) decreases (since velocity is getting closer to zero). So this object is slowing down.

- Third graph: velocity (y-axis) starts at 0 and goes upward (positive velocity) with a constant slope (positive acceleration). Velocity is positive, acceleration is positive (same direction), so speed increases. So this object is speeding up.

Therefore, the graphs that represent objects speeding up are the first and third graphs. But wait, maybe the first graph: if velocity is negative, is it "speeding up" or "speeding down"? Wait, speed is the magnitude, so if velocity is -5 and becomes -10, speed is 5 then 10, so speeding up. So yes, both first and third. But maybe the problem's options: let's check the original problem. The user's image shows three graphs:

1. First graph: velocity (y) vs time (x), line from (0,0) down (negative velocity, increasing magnitude).

2. Second graph: velocity (y) is negative, line up (towards zero, decreasing magnitude).

3. Third graph: velocity (y) from 0 up (positive velocity, increasing magnitude).

So the correct ones are the first and third? Wait, but maybe I made a mistake. Let's recall: speeding up means that the magnitude of velocity is increasing. So:

- If velocity is positive and increasing (third graph): speed increases → speeding up.

- If velocity is negative and decreasing (i.e., becoming more negative, first graph): speed increases (since |-5| =5, |-10|=10) → speeding up.

- If velocity is negative and increasing (towards zero, second graph): speed decreases (|-5|=5, |-2|=2) → slowing down.

So yes, first and third graphs are speeding up. But maybe the problem's options: let's see the user's image. The three graphs:

1. First graph: tap to select.

2. Second graph: tap to select.

3. Third graph: tap to select.

So the answer is the first and third graphs. Wait, but maybe the first graph: when velocity is negative, is it considered "speeding up"? Let's confirm with physics: when the acceleration and velocity have the same sign (both positive or both negative), the object is speeding up. When they have opposite signs, slowing down.

First graph: velocity is negative (v < 0), acceleration is negative (a < 0, since slope is negative) → same sign → speeding up.

Third graph: velocity positive (v > 0), acceleration positive (a > 0, slope positive) → same sign → speeding up.

Second graph: velocity negative (v < 0), acceleration positive (a > 0, slope positive) → opposite signs → slowing down.

Therefore, the objects speeding up are the first and third graphs.

Answer:

The first graph (velocity starting at 0 and going negative with increasing magnitude) and the third graph (velocity starting at 0 and going positive with increasing magnitude) represent objects that are speeding up. So tap on the first and third graphs.