Two cyclists, Isabella and Maria, are having a race. They both travel along a straight road with constant acceleration, starting from rest at point $$\(A\)$$. Isabella accelerates for $$\(5 \mathrm{~s}\)$$ at a constant rate $$\(a \mathrm{~m} \mathrm{~s}^{-2}\)$$. She then travels at the constant speed she has reached for $$\(10 \mathrm{~s}\)$$, before decelerating to rest at a constant rate over a period of $$\(5 \mathrm{~s}\)$$. Maria accelerates at a constant rate, reaching a speed of $$\(5 \mathrm{~m} \mathrm{~s}^{-1}\)$$ in a distance of $$\(27.5 \mathrm{~m}\)$$. She then maintains this speed for a period of $$\(10 \mathrm{~s}\)$$, before decelerating to rest at a constant rate over a period of $$\(5 \mathrm{~s}\)$$. Find the value of $$\(a\)$$ for which the two cyclists travel the same distance. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

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