Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
Cyclists $P$ and $Q$ move along the straight road $ABC$, setting off together from $A$ and reaching $C$ at the same time. They each pass through $B$ $400\,\text{s}$ after leaving $A$. Cyclist $P$ begins with speed $3\,\text{m s}^{-1}$ and then increases this speed with constant acceleration $0.005\,\text{m s}^{-2}$ until he arrives at $B$.
(i)[3]
Demonstrate that $AB$ equals $1600\,\text{m}$ and determine $P$’s speed at $B$.
(ii)[6]
Cyclist $Q$ moves from $A$ to $B$ with speed $v\,\text{m s}^{-1}$ at time $t$ seconds after leaving $A$, where $v = 0.04t - 0.0001t^2 + k$, and $k$ is a constant. Determine the value of $k$ and the maximum speed of $Q$ before he has reached $B$.
(iii)[4]
Cyclist $P$ goes from $B$ to $C$, covering $1400\,\text{m}$ at the speed reached at $B$. Cyclist $Q$ travels from $B$ to $C$ with constant acceleration $a\,\text{m s}^{-2}$. Determine the time for the journey from $B$ to $C$ and determine the value of $a$.
Worked solution & mark scheme
This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: “By applying $s = ut + \frac{1}{2}at^2$ or $v = u + at$” …