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June 2021 p41 q4
3826
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 s at a constant rate \(a \text{ m s}^{-2}\). She then travels at the constant speed she has reached for 10 s, before decelerating to rest at a constant rate over a period of 5 s.
Maria accelerates at a constant rate, reaching a speed of 5 \(\text{ m s}^{-1}\) in a distance of 27.5 m. She then maintains this speed for a period of 10 s, before decelerating to rest at a constant rate over a period of 5 s.
(a) Given that \(a = 1.1\), find which cyclist travels further.
(b) Find the value of \(a\) for which the two cyclists travel the same distance.
Solution
(a) For Isabella, the acceleration phase gives a final speed \(v = 5 \times 1.1 = 5.5 \text{ m s}^{-1}\). The total distance \(s_I\) is calculated as: