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Select the velocity–time graph that best matches the following description of motion.
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A boat moves at constant speed through the water, then accelerates for a short time, and then continues moving at a higher constant speed.
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In this question, we are presented with five different velocity–time graphs.
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And we want to find the velocity–time graph that best matches the description of motion given in the question.
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Let’s break up the description of motion into smaller parts, and we will consider how each part of the description will be represented on a velocity–time graph.
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The boat initially moves at a constant speed through the water.
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If an object is moving at a constant speed, then this means that the object’s velocity must have a constant magnitude.
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On a velocity–time graph, a velocity with a constant magnitude will be represented by a straight horizontal line parallel to the time axis.
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For a line like this, all the different time values on the 𝑥-axis correspond to the same value of velocity on the 𝑦-axis.
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If we look at the five velocity–time graphs, we can see that graphs (A), (B), and (D) do not initially begin with a straight horizontal line.
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Instead, these three graphs begin with lines that have a constant positive gradient.
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This shows the velocity the boat increasing with time, which means that the boat would be accelerating during this time interval.
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This does not match the initial description of motion for the boat, so this means that graphs (A), (B), and (D) are incorrect.
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Graphs (C) and (E) do begin with a straight horizontal line parallel to the time axis, so these two graphs match the initial description of motion.
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The next part of the description says the boat accelerates for a short time.
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On a velocity–time graph, this would be represented by a line with a positive gradient.
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As the time value increases on the axis, so does the value of the velocity.
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In graph (C), this part of the graph is straight and has a positive gradient, which indicates a constant value of acceleration.
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In graph (E), the line is curved but still maintains a positive gradient throughout.
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This corresponds with a changing value of acceleration.
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The description of motion does not say whether the acceleration of the boat is constant or changing, so graphs (C) and (E) still match the description of motion up to this point.
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Now let’s consider the final part of the description of motion, which says the boat continues to move at a higher constant speed.
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Similar to the initial part of the description of motion, a constant speed will mean that the boat’s velocity must have a constant magnitude, which corresponds to a straight horizontal line parallel to the time axis on a velocity–time graph.
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However, the boat is now moving at a higher constant speed than it was at the start.
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This means that the straight horizontal line should be higher up on the velocity axis than the line representing the boat’s initial motion.
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In graph (E), this final line has a constant positive gradient indicating that the boat is accelerating during this time interval.
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This does not match the final part of the description of motion for the boat, so graph (E) is incorrect.
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Graph (C) does have a straight horizontal line during this final motion.
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This horizontal line is higher than the horizontal line representing the boat’s initial motion, which indicates a higher constant speed.
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This matches the final part of the description of motion, and so graph (C) must be the correct answer.
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Graph (C) best matches the description of motion.