9709 P42 - Nov 2024 - Q6 - 10 marks
9899
Take \(g=10\,\mathrm{m\,s^{-2}}\). A particle P starts from O with velocity \(6\,\mathrm{m\,s^{-1}}\). Its acceleration in \(\mathrm{m\,s^{-2}}\) is \[a=-1.5t^{1/2}\quad(0\le t\le1),\qquad a=1.5t^{1/2}-3t^{-1/2}\quad(t>1).\]
(a) Find its velocity at t=1. [3]
(b) Velocity is continuous at t=1. Find its velocity for t>1. [3]
(c) Velocity is positive up to t=4. Find the total distance travelled between t=0 and t=4. [4]
