A specialized robotic track-crawler of weight 1800 N is moving at a speed vvv. The total resistive force, FFF, opposing the motion of the crawler is modeled by the formula
F=kv2 F = k v^2 F=kv2where k k\,k is a constant.
The crawler is allowed to coast from rest down a track inclined at 5.0∘ 5.0^\circ\,5.0∘ to the horizontal. The engine of the crawler is switched off. The crawler eventually reaches a maximum speed of 14 m s-1.
Sketch a graph to show how the speed of the crawler changes over time. Describe the key features of this graph and state the value of its horizontal asymptote.
Explain why the crawler reaches a maximum speed.
Show that the value of k k\,k in the equation F=kv2F = kv^2F=kv2 is approximately 0.80 N s2 m-2.
The crawler is now moving along a straight, horizontal section of track. The engine of the crawler delivers a maximum power of 21.6 kW. Calculate the maximum speed of the crawler.
Upgrades are made to the engine of the crawler so that it can produce double the original maximum power. Explain why the maximum speed of the modified crawler is not doubled.
