When acceleration is NOT constant, kinematic equations (SUVAT) fail. Use:

Fundamental relations:

• v = $\frac{ds}{dt}$ => ds = vdt => s = integral of vdt
• a = $\frac{dv}{dt}$ => dv = adt => v = integral of adt
• a = vdv/ds => vdv = a*ds (useful when a = f(s))

Common JEE cases:

1. a = f(t): Integrate adt to get v(t), then integrate vdt to get s(t)
2. a = f(v): Use dt = $\frac{dv}{a}$ or ds = v*dv/a
3. a = f(s): Use vdv = ads, integrate to get v(s)

Example: If a = 2t, then v = integral(2t*dt) = $t^2$ + C. If v(0) = 0, then v = $t^2$. Then s = integral($t^2$*dt) = $t^3$/3 + C'. If s(0) = 0, then s = $t^3$/3.