(i)[5]
Determine $A$ and show that $B = 3375$.
(ii)[3]
Find a formula in terms of $t$ for the vehicle's total distance travelled when $t > 15$.
(iii)[3]
Determine the speed of the vehicle when the total distance covered is $315 \text{ m}$.
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 $v \text{ m s}^{-1}$ at time $t \text{ s}$ after it begins is given by $$v = A(t - 0.05t^{2}) \text{ for } 0 \le t \le 15,$$ $$v = \frac{B}{t^{2}} \text{ for } t > 15,$$ where $A$ and $B$ are constants. The distance the vehicle covers from $t = 0$ to $t = 15$ is $225 \text{ m}$.