A small motorized cart of weight 2400 N2400\text{ N}2400 N is moving at speed vvv. The total resistive force, FFF, acting against the motion of the cart is given by the formula
F=kv2 F = k v^2 F=kv2where kkk is a constant.
The cart is allowed to roll from rest down a slope of 4.0∘4.0^\circ4.0∘ to the horizontal. The engine of the cart is not switched on. The cart reaches a maximum speed of 13 m s−113\text{ m s}^{-1}13 m s−1. 
Sketch a graph to show how the speed of the cart changes over time. Describe the key features of this graph and state the value of its horizontal asymptote.
Explain why the cart reaches a maximum speed.
Show that the value of kkk in the equation F=kv2F = kv^2F=kv2 is about 1.0 N s2 m−21.0\text{ N s}^2\text{ m}^{-2}1.0 N s2 m−2.
The cart is now moving along a straight, level track. The engine of the cart delivers a maximum power of 27 kW27\text{ kW}27 kW. Calculate the maximum speed of the cart.
Changes are made to the engine of the cart so that it can produce double the original maximum power. Explain why the maximum speed of the modified cart is not doubled.
