CSEC Additional Mathematics · 2014 · Paper 2 · Question 8(b)(iii)

A particle travels along a straight line. It starts from rest at a point, P, on the line and after 10 seconds, it comes to rest at another point, Q, on the line. The velocity v m s⁻¹ at time t seconds after leaving P is v = 0.72t² - 0.096t³ for 0 ≤ t ≤5 and v = 2.4t-0.24t² for 5 ≤ t ≤ 10. At maximum velocity the particle has no acceleration.

Find the distance moved by the particle from P to the point where the particle attains its maximum velocity.