Question

3. If the time and displacement of particle along the positive
X-axis are related ast = (x2 - 1)2, then find the acceleration
in terms of x.​

Answer 1

a= 1/x³

Explanation:

the relation between time and the displacement is given by the equation ,

t = (x²-1)½

t²= x² - 1 .....(1)

x² - t² = 1 ............(2)

differentiate equation(1) with respect to time,

2t = 2x dx/dt

velocity, v = dx/dt

2t = 2xv

v= t/x ........(3)

again differentiate the above equation ,

2 = 2(x dx²/dt² + dx/dt . dx/dt)

Acceleration, a= dx²/ dt²

1 = xa + v²

xa = 1 - v²

xa = 1 - t²/ x²( from equation 3)

xa = x² - t²/ x²

= 1/x² ( from equation 2)

Acceleration, a = 1/x³