The position of a particle moving rectilinearly is given by x = t3-3t2-10. Find the distance travelled by the particle in the first 4 seconds starting from t = 0.

x = t3-3t2-10v = dxdt = 3t2-6tNow, v = 0 gives      t = 0  and t = 2 sec.Velocity will become zero at t = 2 sec., so particle will change direction after t = 2 sec.At t = 0   x(o sec) = -10At t = 2 sec.   x(2 sec) = 23-3(2)2-10 =  8-12-10 = -14At t = 4 sec.    x(4 sec) = 43-3(4)2-10                 = 64-48-10 = 6Distance travelled = x1+x2       = |-14-(-10)|+|6-(-14)| = 4 + 20 = 24Distance travelled = 24 units.