When acceleration varies with time, position, or velocity, SUVAT equations fail. Use calculus:

a = f(t): Integrate a with respect to t to get v(t), then integrate v(t) to get x(t).

• v = integral(a*dt) + $v_0$
• x = integral(v*dt) + $x_0$

a = f(v): Separate variables.

• dt = $\frac{dv}{a}$ => t = integral$\frac{dv}{a}$
• OR: ds = v*dv/a => s = integral$\frac{v*dv}{a}$

a = f(x): Use vdv = adx.

• integral(vdv) = integral(adx)
• \frac{1}{2}$$v^2 = integral(a*dx) + constant

Maximum velocity: Occurs when a = 0 (acceleration changes from positive to negative).

JEE Strategy: Identify which variable a depends on, choose the right differential form, separate variables, and integrate with initial conditions.