Solution:

Concept: Particle comes to rest when velocity is zero. Velocity \( v = \frac{dx}{dt} = 12 - 3t^2 \). Setting \( v=0 \) gives \( 12 - 3t^2 = 0 \), so \( t=2 \text{ s} \). Initial position at \( t=0 \) is \( x(0) = 40 \text{ m} \). Position at \( t=2 \) s is \( x(2) = 40 + 12(2) - (2)^3 = 56 \text{ m} \). Distance traveled is \( |x(2) - x(0)| = |56 - 40| = 16 \text{ m} \).