(a)[4]
Using the fact that $P$ is never at instantaneous rest, show that $k > 4.5$.
(b)[6]
If $k = 2.5$ instead, find the total distance travelled by $P$ for $1 \leq t \leq 3$.
Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
Particle $P$ travels along a straight line. After it leaves point $O$ on the line, the acceleration $a\,\text{m s}^{-2}$ of $P$ at time $t$ is $a = kt - 3$, where $k$ is a positive constant. When $t = 0$, the velocity of $P$ is $1\,\text{m s}^{-1}$.