The position (x) of a particle moving along x axis varies with time t

1.	The position (x) of a particle moving along x axis varies with time t as t=√3-3, where all quantities are in SI units. If displacement of the particle in time duration t=0 to t=5 s, is D, then find value of (D - 50) in m.help
Answer» $\implies\rm t = \sqrt{x} -3$ •• differentiating both sides. $\implies \rm dt = \dfrac{1}{2}\times \dfrac{1}{\sqrt{x}}.dx - 0$ $\implies \rm \dfrac{dx}{dt}= 2\sqrt{x}$ $\implies \bf v = 2\sqrt{x}$ We KNOW that, a = v.dv/dx $\implies \rm v = 2\sqrt{x}$ $\implies \rm dv= 2\times \dfrac{1}{2\: \sqrt{x}} .dx$ $\implies \rm \dfrac{dv}{dx}= \dfrac{1}{\sqrt{x}}$ $\to\rm v.\dfrac{dv}{dx} = 2\sqrt{x}\times \dfrac{1}{\sqrt{x}}$ $\to \bf a = 2 ms^{-2}$ ★ As acceleration is constant, displacement by equation of motion: s = UT +½(a)t² D = 0 + ½(2){(5)²-(0)²} D = 25 》 D - 50 = 25 - 50 = -25m