An automobile of mass travels along a straight highway in two successive segments
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
An automobile of mass m travels along a straight highway in two successive segments.
• Segment I: The car ascends a section of road that is inclined at a constant angle θ above the horizontal. It starts this segment with speed v0, ends with the same speed v0, and spends a time t1 on the incline.
• Segment II: Immediately after reaching level ground at the top of the incline, the car accelerates in a straight line from speed v0 to speed 2v0 in a time t2.
Assume air resistance and frictional losses are negligible and that the engine provides all necessary mechanical energy.
(a) Derive an expression, in symbols only, for the average mechanical power that the engine must deliver during Segment I.
(b) Derive an expression, in symbols only, for the average mechanical power that the engine must deliver during Segment II.
(c) Given that t1=t2 and that the vertical height gained in Segment I is h=2gv02, determine which segment requires the greater average engine power. Provide a clear comparison supported by algebraic reasoning.
(d) Discuss one physical factor not considered in the analysis above that could alter the actual power required by the engine in real-world driving.