Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
The diagram presents a velocity-time graph that represents the motion of a tractor. It is made up of four straight-line sections. The tractor passes through point $O$ at time $t = 0$ with speed $U$ m s$^{-1}$. It then increases in speed to $V$ m s$^{-1}$ over $5$ s, after which it continues at that speed for another $25$ s. Next, the tractor accelerates to $12$ m s$^{-1}$ over $5$ s. It then slows down to zero in $15$ s.
(a(i))[2]
With the tractor’s acceleration from $t = 30$ to $t = 35$ stated as $0.8$ m s$^{-2}$, determine $V$.
(a(ii))[3]
Also given that the tractor travels $375$ m in the $50$ s of motion, find $U$.
(i)[2]
With the tractor’s acceleration from $t = 30$ to $t = 35$ given as $0.8\ \text{m s}^{-2}$, find $V$.
(ii)[3]
Also given that the tractor covers $375\ \text{m}$ in the $50$ seconds of motion, find $U$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Form an equation in $v$ by using the graph gradient or the constant acceleration formula” …