Two trains, A A\,A and BBB, are moving in the same direction along the same straight horizontal track.
Train A A\,A moves with constant speed 20 m s−1^{-1}−1.
At a certain instant train B B\,B is 500 metres behind train A A\,A and is moving with speed 35 m s−1^{-1}−1.
At that instant the driver of B B\,B applies the brakes, producing a constant deceleration of magnitude d d\,d m s−2^{-2}−2.
Take the position of B B\,B at that instant as the origin, and let t t\,t be the time in seconds measured from that instant.
Show that the two trains meet only if 12dt2−15t+500=0\displaystyle \frac12dt^2 - 15t + 500 = 021dt2−15t+500=0.
Hence find the value of d d\,d for which B B\,B just avoids colliding with AAA.
State one modelling assumption you have made.
265 exam-style questions on AQA A Level Maths 3.2 Q: Kinematics, covering 3.2.1 Language of kinematics, 3.2.2 Graphs in kinematics, 3.2.3 Constant acceleration formulae, 3.2.4 Calculus in kinematics (A-level only), and 3.2.5 Motion under gravity and projectiles (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.