The displacement of a particle at time $t$ seconds is given by $s = t^3 - 6t^2 + 9t + 4$ metres. The particle is momentarily at rest when $t$ equals

The particle is at rest when velocity v = ds/dt = 0. Differentiating: v = 3t² - 12t + 9 = 3(t² - 4t + 3) = 3(t - 1)(t - 3) = 0, giving t = 1 or t = 3. Options B, C, and D result from errors in factorising the quadratic or differentiating the displacement function.