Question

derive the equation for motion for non uniform motion in One dimension​

Answer 1

Following are the derived equations of motion in one dimension.

Explanation:

In order to derive equations of motion for one dimensional non-uniform motion.  Let's say we have  s,v and a as displacement, velocity and acceleration at time t.

• As we know that the acceleration is constant.

a = dv/ dt ⇒ dv = adt.

v=∫adt = at+C1.

The initial velocity is u.  when t = 0

• v = u+at.

v = ds/dt = u+at

ds = (u+at)dt.

S = ∫(u+at)dt=ut+1/2at^2+C2.

• We assume that when t=0, the initial displacement is 0.

• S = ut+1/2at^2.

v=u+at

t = v− ua.

S = u(v−u/a) + 1/2a(v−u/a)2.

2as = 2uv−2u2+v2−2uv+u2

2as = −u2+v2.

• V^2 = u^2+2as.

v=u+at

a=v−ut.

S=ut+1/2(v−u/t)t2 = ut+1/2(v−u)t.

• S=1/2(u+v)t.

v=u+at

u=v−at.

S=(v−at)t+1/2at2=vt−at2+1/2at2.

• S=vt−1/2at2.

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Answer 2

Answer:

s=½ (u+v)t

u=v–at .S=(v–at) t + ½ at 2 = vt – at 2 + ½ at 2