The acceleration of a car moving along a straight test track is modelled by a=(kt−4) m s−2a=(kt-4)\text{ m s}^{-2}a=(kt−4) m s−2 for 0≤t≤40\leq t\leq40≤t≤4, where k k\,k is a constant. At t=0t=0t=0 the car has velocity 10 m s-1, and at t=4t=4t=4 it has velocity 2 m s-1.
Determine kkk.
Find the minimum speed of the car during the four seconds.
Determine the distance travelled during the four seconds.
State one limitation of this model for a real car.
260 exam-style questions on OCR A Level Maths 3.2 Kinematics, covering 3.2.1 Language of kinematics, 3.2.2 Graphs in kinematics, 3.2.3 Displacement-time and velocity-time graphs, 3.2.4 Constant acceleration formulae, 3.2.5 Constant acceleration in two dimensions (A-level only), 3.2.6 Non-uniform acceleration in one dimension (A-level only), 3.2.7 Non-uniform acceleration in two dimensions (A-level only), 3.2.8 Motion under gravity using vectors (A-level only), and 3.2.9 Projectiles (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.