Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A vehicle travels along a straight line. Its velocity $v\,\text{m s}^{-1}$, measured at time $t\,\text{s}$ after the start of motion, is defined by $v = A(t - 0.05t^2)$ for $0 \le t \le 15$, and by $v = \frac{B}{t^2}$ for $t > 15$, where $A$ and $B$ are constants. The distance covered by the vehicle from $t = 0$ to $t = 15$ is $225\,\text{m}$.
(a(i))[5]
Determine $A$ and show that $B = 3375$.
(a(ii))[3]
Give an expression, in terms of $t$, for the vehicle's total distance travelled when $t > 15$.
(a(iii))[3]
Determine the speed of the vehicle when the total distance covered is $315\,\text{m}$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Deriving $s_1$ by integrating $v_1$” …