Question

derive the following equations;
a] v=u+at
b]v^2=u^2+2as
c]S=ut+1/2at^2

Answer 1

Answer:

(a) Let the initial velocity of a body be u, final velocity after acceleration for time t be v, acceleration be a.

We know rate of change of velocity is called acceleration.

Therefore, a = (v - u) / t

at = v - u

v = u + at

(b) If a particle with initial velocity u, acceleration a attains final velocity v after time t, then average velocity will be (u + v)/2

Hence the particle can be considered to have travelled a distance s with average velocity (u+v) / 2 in time t

Therefore s = (u+v)/2 × t

s = {u + (u+at)} /2 ×t

where v=u+at

s = (2ut + at²)/2

s = 2ut/ 2 + at²/2

s = ut + 1/2 at²

(c) We know, v = u + at

Squaring both sides,

v² = (u + at)²

v²= u² + a²t² + 2atu

v²= u² + 2a( 1/2at² + ut)

v² = u² + 2as where s= ut + 1/2at²