(a)[7]
Determine the value of $k$. Hence obtain an expression, in terms of $t$, for the particle's displacement from $A$.
(b)[4]
Determine the displacement of the particle from $A$ when its velocity is at a minimum.
Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A particle travels along the straight line $AB$. Its velocity $v\,\text{m s}^{-1}$ after $t\,\text{s}$ from leaving $A$ is $v = k(t^2 - 10t + 21)$, where $k$ is a constant. When $t = 3$, the particle's displacement from $A$, measured towards $B$, is $2.85\,\text{m}$, and when $t = 6$ it is $2.4\,\text{m}$.