An object moving with initial velocity *u *along a straight line attains maximum velocity *v *after travelling distance *s*. Assume the acceleration is uniform. Derive the relationship between position and velocity of the object by graphical method.

Please answer

From graph , acceleration, a = slope of velocity-time graph AB

a = DB/AD =DB/t or DB = at

Now distance travelled by object in time t is

S = area of trapezium OABE

= area of rectangle OADE + area of triangle ADB

= OA*OE+1/2 DB*AD

= ut+1/2 at

^{2}

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