A velocity-time graph for a body moving with uniform acceleration is a straight line that slopes upwards. What does the area under this line between two time points represent?
The displacement of the body during that time interval
For uniform acceleration the velocity–time line is straight, and the region under it between two instants is a trapezium whose parallel sides are the initial and final velocities and whose width is the elapsed time.
Its area equals (average velocity) × (time), which is exactly the length moved in that interval, so the enclosed area measures how far the body has gone.
The change in velocity is read off the vertical axis and the acceleration is the slope of the line, neither of which is an area.
Hence, the answer is The displacement of the body during that time interval.
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Important Questions from Motion
An object is covering distance in direct proportion to the square of time elapsed. What conclusion can be drawn about the motion of the object?
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