Paper 5 October/November 2010 MATHEMATICS (9709/53) A Levels
لطفا برای اطمینان از عملکرد و تجربه بهتر از مرورگرهای مدرن و به روز مانند کروم یا فایرفاکس استفاده کنید.

A particle $P$ starts from rest at a point $O$ and travels in a straight line. The acceleration of $P$ is $\left( {15 - 6x} \right){\text{ }}m{\text{ }}{s^{ - 2}}$, where $x{\text{ }}m$ is the displacement of $P$ from $O$.
a) Find the value of $x$ for which $P$ reaches its maximum velocity, and calculate this maximum velocity.
b) Calculate the acceleration of $P$ when it is at instantaneous rest and $x \gt 0$.