velocity-time graph

over what interval(s) is the displacement of the object negative?

from 30-40 seconds

from 25-30 seconds

from 25-40 seconds

from 0-10 seconds and from 20-25 seconds

Question

velocity-time graph

over what interval(s) is the displacement of the object negative?

from 30-40 seconds

from 25-30 seconds

from 25-40 seconds

from 0-10 seconds and from 20-25 seconds

Accepted Answer

# Brief Explanations:
In a velocity - time graph, the displacement is given by the area under the velocity - time curve. If the velocity is negative, the area (displacement) will be negative. We need to find the time interval where the velocity is negative (since velocity is on the y - axis, negative velocity is below the time axis (x - axis)). Looking at the graph, the velocity is negative from 25 - 40 seconds? Wait, no, let's re - examine. Wait, the options: Let's recall that in a velocity - time graph, when velocity is positive, displacement is positive (area above x - axis), when velocity is negative, displacement is negative (area below x - axis). So we need to find when velocity is negative. From the graph, after 25 seconds (assuming the crossing of x - axis is around 25 - 30? Wait, the option "From 25 - 40 seconds" – wait, no, let's check the options again. Wait, the options are:

1. From 30 - 40 seconds
2. From 25 - 30 seconds? No, the second option is "From 25 - 30 seconds"? Wait, no, the user's image: the options are "From 30 - 40 seconds", "From 25 - 30 seconds"? Wait, no, the user's text: "From 30 - 40 seconds", "From 25 - 30 seconds" (maybe typo, maybe 25 - 30? Wait, no, the original options:

Wait, the user's problem:

Options:

- From 30 - 40 seconds

- From 25 - 30 seconds (maybe 25 - 30? Wait, no, the user wrote "From 25 - 40 seconds" and "From 0 - 10 seconds and from 20 - 25 seconds"

Wait, the key is: In a velocity - time graph, displacement is the integral of velocity with respect to time, which is the area under the velocity - time curve. When velocity is negative (below the time axis), the area (displacement) is negative. So we look for the time interval where velocity is negative.

Looking at the graph, the velocity goes below the x - axis (becomes negative) after some time (around 25 - 30? Wait, the option "From 25 - 40 seconds" – let's check the options again. Wait, the correct option should be the one where velocity is negative. Let's analyze each option:

- From 30 - 40 seconds: If velocity is negative here, but maybe not the full interval.

- From 25 - 30 seconds: Maybe too short.

- From 25 - 40 seconds: This interval includes the time when velocity is negative (below x - axis), so the area (displacement) here will be negative because velocity is negative.

- From 0 - 10 seconds and from 20 - 25 seconds: In these intervals, velocity is positive (above x - axis), so displacement is positive.

Wait, but the user's selected option in the image is "From 25 - 30 seconds"? No, the user's image shows a radio button on "From 25 - 30 seconds"? Wait, no, the user's text:

"From 30 - 40 seconds

From 25 - 30 seconds

From 25 - 40 seconds

From 0 - 10 seconds and from 20 - 25 seconds"

Wait, maybe a typo. Let's think again. The velocity - time graph: initially, velocity increases from 0 to 10 seconds (positive), then constant from 10 - 25 seconds (positive), then decreases, crosses zero (at around 25 - 30 seconds), then becomes negative (below x - axis) until 30 - 40? Wait, no, the graph then comes back up. Wait, the graph after 25 seconds: velocity goes negative (below x - axis) from, say, 25 to 40? Wait, no, the last part of the graph is from 30 to 40, velocity is increasing from negative to zero? Wait, maybe the correct interval is when velocity is negative, so the area (displacement) is negative. So the time when velocity is negative is when the graph is below the time axis (x - axis). So looking at the options, "From 25 - 40 seconds" – because in this interval, part of it (after crossing zero) has negative velocity, so the displacement (area) will be negative. Wait, but maybe the correct option is "From 25 - 40 seconds". Wait, no, let's check the options again.

Wait, the problem is to find when displacement is negative. Displacement is negative when the area under velocity - time curve is negative, which happens when velocity is negative (since area is integral of velocity, and if velocity is negative, integral is negative). So we need to find the time interval where velocity is negative.

Looking at the graph:

- 0 - 10 seconds: velocity increasing from 0 to positive, so velocity positive, displacement positive.

- 10 - 25 seconds: velocity constant (positive), displacement positive.

- 25 - 30 seconds: velocity decreasing from positive to zero, then negative? Wait, no, the graph crosses zero (velocity = 0) at some point between 25 - 30, then goes negative (below x - axis) until, say, 30 - 40, then comes back up to zero at 40.

Wait, the option "From 25 - 40 seconds": in this interval, after crossing zero (velocity becomes negative), the area (displacement) will be negative because velocity is negative. So the displacement is negative when velocity is negative, i.e., when the graph is below the x - axis. So the interval when velocity is negative is from when it crosses zero (around 25) until it comes back to zero (around 40). So the interval is 25 - 40 seconds.

Wait, but the options:

- From 30 - 40 seconds: maybe part of it, but not the full interval.

- From 25 - 30 seconds: maybe when velocity is decreasing from positive to negative, but displacement is still positive until velocity becomes negative? No, displacement is the integral. Let's think of velocity as a function v(t). Displacement s(t)=$\int_{t_1}^{t_2}v(t)dt$. If v(t) is positive, s is positive; if v(t) is negative, s is negative.

So when does v(t) become negative? After crossing the t - axis (v = 0). So the time when v(t)<0 is the interval where the graph is below the t - axis. From the graph, that's from, say, 25 to 40 seconds (assuming the graph crosses zero at 25, goes negative until 30, then comes back up? Wait, no, the last part of the graph is a triangle from 30 to 40, with velocity going from negative to zero. So the velocity is negative from 25 (when it crosses zero going down) to 40 (when it comes back to zero). So the interval is 25 - 40 seconds. So the correct option is "From 25 - 40 seconds".

# Answer:
From 25 - 40 seconds

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