Question

What is the quantity which is measured by the area occupied below the velocity-time graph?

Answer 1

Distance

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

Where,

Length = t

Breath = v

Area = vt = velocity × time …(i)

We know,

`"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.