Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line

Kinematics of motion in a straight line — practice question

Two cyclists, Isabella and Maria, are racing. Each one moves along a straight road with constant acceleration, beginning from rest at point $A$. Isabella accelerates for $5\,\text{s}$ at a steady rate of $a\,\text{m s}^{-2}$. After that, she continues at the constant speed she has reached for $10\,\text{s}$, and then she slows to rest at a constant rate over $5\,\text{s}$. Maria accelerates at a constant rate until she reaches $5\,\text{m s}^{-1}$ over a distance of $27.5\,\text{m}$. She then keeps this speed for $10\,\text{s}$ before decelerating to rest at a constant rate over $5\,\text{s}$.
(a)[5]

If $a = 1.1$, decide which cyclist covers the greater distance.

(b)[2]

Determine the value of $a$ for which both cyclists cover the same distance.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Work out Isabella’s speed, $v=5\times1.1=5.5$

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