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

Fundamental relations:

• v = ds/dt => ds = vdt => s = integral of vdt
• a = 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 = 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(2tdt) = t^2 + C. If v(0) = 0, then v = t^2. Then s = integral(t^2dt) = t^3/3 + C'. If s(0) = 0, then s = t^3/3.