Question

the roller coaster ride starts with the car at rest at point a rank from greatest to least the cars a. speed at each point b. kinetic energy c. potential energy

Explanation:

Step1: Analyze potential energy

Potential energy \(U = mgh\) (where \(m\) is mass, \(g\) is acceleration due to gravity, \(h\) is height). Higher the height \(h\), greater the potential energy. So potential energy ranking: \(A>E>C>B>D\)

Step2: Analyze kinetic energy

By conservation of mechanical energy \(E = K+U\) (where \(E\) is total mechanical energy, \(K\) is kinetic energy). Since \(E\) is constant (assuming no non - conservative forces like friction), \(K=E - U\). So kinetic energy ranking is opposite of potential energy ranking. \(K\propto\frac{1}{U}\) (for constant \(E\)). So \(K\) ranking: \(D>B>C>E>A\)

Step3: Analyze speed

Since \(K=\frac{1}{2}mv^{2}\), \(v=\sqrt{\frac{2K}{m}}\). So speed ranking is same as kinetic energy ranking. \(v\propto\sqrt{K}\). So \(v\) ranking: \(D>B>C>E>A\)

Answer:

A. Speed: \(D>B>C>E>A\)
B. Kinetic energy: \(D>B>C>E>A\)
C. Potential energy: \(A>E>C>B>D\)