Derive s=ut+1/2at 2

1.	Derive s=ut+1/2at 2
Answer» RONG> ⇒To prove s=ut + 1/2at² FIRST we have to prove v = u +at Derivation ⇒ For one DIMENSIONAL MOTION with a = constant We can write as dv = a dt Integrating both sides , we have $\rm \implies \int dv = a \int dt$ At t = 0 , velocity is u and at t = t velocity is v . HENCE $\rm\implies\int\limits^v_u {} \, dv=a\int\limits^t_0 {} \, dt$ $\rm\implies [v]^v_u= a[t]^t_o$ $\implies\rm v-u=at$ $\boxed{\rm v=u +at}$ we can write as ds = v dt = (u +at)dt At time t=0 suppose s = 0 and at t = t , displacement is s , the $\rm \implies \int\limits^s_0 {} \, ds=\int\limits^t_0 {} \,(u + at) dt$ $\rm\implies [s]^s_0=\bigg[ut +\dfrac{1}{2} at^{2} \bigg]^t_0$ $\boxed{\rm s= ut+\dfrac{1}{2} at^{2} }$ Hence proved

Answer» RONG>

⇒To prove s=ut + 1/2at² FIRST we have to prove v = u +at