(a)[6]
It is stated that the velocities of $X$ and $Y$ are the same when they collide. Calculate the distance $AB$.
(b)[2]
Instead, $AB = 36\,\text{m}$ is given. Verify that $X$ and $Y$ collide after $3\,\text{s}$.
Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
Particles $X$ and $Y$ travel along a straight line through points $A$ and $B$. Particle $X$ begins from rest at $A$ and heads towards $B$. At the same instant, $Y$ begins from rest at $B$.
After $t$ seconds from the start of motion:
• the acceleration of $X$ in the direction $AB$ is $(12t + 12)\,\text{m s}^{-2}$,
• the acceleration of $Y$ in the direction $AB$ is $(24t - 8)\,\text{m s}^{-2}$.