(a)[6]
Show that the values are $k = 3$ and $p = 26$.
(b)[5]
Find the distance travelled by the particle from the time when its acceleration is zero to the time when its velocity becomes zero.
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 a straight line. Its velocity $v\,\text{m s}^{-1}$, $t\,\text{s}$ after it leaves a fixed point $O$, is defined by $v = k(20 + pt - 6t^2)$, where $k$ and $p$ are constants. At $t = 1$, the particle has acceleration $42\,\text{m s}^{-2}$ and displacement from $O$ equal to $93\,\text{m}$.