The area under the velocity-time graph for a particle moving in a stra

The area under the velocity-time graph for a particle moving in a straight line with uniform acceleration gives

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its average velocity

its net displacement

the distance travelled by it

its average speed

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This question was previously asked in

UPSC CDS-1 – 2023

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For a particle moving in a straight line, the area under the velocity-time graph represents the displacement of the particle during the given time interval. If the velocity is plotted on the y-axis and time on the x-axis, the area under the curve between two time points gives the change in position (displacement) over that period. This is valid even if the velocity is non-uniform or changes direction.

The area under the velocity-time graph represents the net displacement.

If the particle moves in only one direction (velocity does not change sign), the magnitude of the displacement is equal to the distance traveled. However, if the velocity-time graph goes below the time axis (indicating motion in the opposite direction), the area below the axis is considered negative displacement. The net displacement is the sum of the signed areas. The total distance traveled would be the sum of the magnitudes of the areas. The question specifies uniform acceleration, which means the graph is a straight line, but it doesn’t preclude the velocity from changing direction (e.g., starting with negative velocity and accelerating in the positive direction).

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