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.