Question

Derive second equation of motion with the use of v - t graph.

Answer 1

Graphical derivation of 2^nd equation of motion:

Distance travelled s = area of trapezium ABDO

⇒ Area of rectangle ACDO + Area of ∆ABC

s = OD × OA + \(\frac{1}{2}\) × BC × AC

= t × u + \(\frac{1}{2}\) (v − u)t

= ut + \(\frac{1}{2}\) (v − u)t.

According to 1^st eqn. of motion

v = u + at 

v − u = at 

∴ s = ut + \(\frac{1}{2}\)at²