CAIE M1 2021 June — Question 4

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2021
SessionJune
TopicSUVAT & Travel Graphs

4 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 \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\). 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 \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) 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 .
  1. Given that \(a = 1.1\), find which cyclist travels further.
  2. Find the value of \(a\) for which the two cyclists travel the same distance.