A particle moves according to x = t³ − 6t² + 9t + 5. How many times does it reverse its direction during 0

Question

A particle moves according to x = t³ − 6t² + 9t + 5. How many times does it reverse its direction during 0<t<4 s?

G1 Physics · Accepted Answer

v = dx/dt = 3t²−12t+9 = 3(t−1)(t−3). Velocity changes sign at both t=1 s and t=3 s. Hence the particle reverses direction twice.