What is the quantity which is measured by the area occupied below the velocity-time graph?
The graph shows the velocity-time graph of a uniformly moving body.
Let the velocity of the body at time (t) be v.
Area of the shaded region = length × breath
Length = t
Breath = v
Area = vt = velocity × time …(i)
`"Velocity" = "Displacement"/"Time"`
∴ Displacement = Velocity × Time…(ii)
From equations (i) and (ii),
Area = Displacement
Hence, the area occupied below the velocity-time graph measures the displacement covered by the body.
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