[Figure: Graph showing speed v vs time t, where vehicle starts from rest at t=0, accelerates uniformly until t=t₁, then continues at constant speed]
The speed v of a vehicle traveling along a straight level road is shown in the above graph. It starts from rest at time t = 0, accelerates uniformly until t = t₁ and then continues at constant speed. At all times the vehicle experiences a retarding force due to friction, which is proportional to its speed. The force f, which must be applied by the engine of the vehicle, is given by:
[Figure: Five different graphs A, B, C, D, E showing different possible relationships between engine force f and time t]