Question

S=ut+½ at² graphically where the symbols have their convention meaning. Deduce the relation?​

Answer 1

Consider a velocity-time graph as shown (above attachment)

The initial velocity u at point A changes at a uniform rate from A to B in time t.

BC is the final velocity v in the graph.

The time t is represented by OC.

The distance travelled by the body is the area under the OABC.

Therefore, distance travelled = area of under OABC = area of rectangle OADC + area of triangle ABD

Area of rectangle OADC and the area of triangle ABD is given as:

Area of rectangle OADC = (OA)(OC) = ut

Area of triangle ABD = (½)(area of rectangle AEBD) = ½ at2

Therefore, distance travelled, s = ut + ½ at2