A particle moves according to x = t³ − 6t² + 9t metre from t=0 to 4 s. Its average speed and average velocity are respectively:

Question

G1 Physics · Accepted Answer

v = 3t²−12t+9 = 3(t−1)(t−3). Turning points are t=1 and 3. Positions: x(0)=0, x(1)=4, x(3)=0, x(4)=4. Total distance = 4+4+4=12 m. Displacement = 4 m. Total time = 4 s. Average speed = 12/4=3 m s⁻¹. Average velocity = 4/4=1 m s⁻¹.