Question

Q5. Show by means of graphical method that :
2
s = ut + 1/2 at
where the symbols have their usual meaning.

Answer 1

Refers to the attachments :

• s = Distance

• u = Initial velocity

• v = Final velocity

• a = Acceleration

• t = time taken

Let the body travels a distance s in time t .

★ Distance travelled by object = Area of trapezium ABDO

= Area of rectangle ACDO + Area of ∆ ABC

Area of triangle ABC = 1/2 × AC × BC

= 1/2 × t × v - u

= 1/2 × t × at [ a = v-u /t ⇒ v-u = at ]

= 1/2 at²

Area of rectangle ABDO = AO × OD

= u × t

= ut

Now,

Dist. travelled = Area of rectangle ACDO + Area of ∆ ABC

s = ut + 1/2 at²