Question

Show that the area under the speed-time graph for a particle moving at a constant speed gives the distance covered by the particles.

Answer 1

The area of a rectangle of sides x and y is given as

A = x*y

now, the area under the v-t curve can be a combination of rectangles, squares and right angle triangles (half rectangles or square). So, the area under the curve in all cases would be a function of x*y for that particular section.

Here x is represented by times and y is represented by velocity. So, the quantity tat is derived by the product of the two, x*y is the displacement s.

So.

s = x*y

this stems from the basic velocity relation.