A girl operates a radio-controlled model car in a vacant parking lot. The girl's position is at the origin of the xy coordinate axes, and the surface of the parking lot lies in the x−y plane. The motion of the car is defined by the position vector r = (2+ 2t³)i + (6 + t³)j, where r and t are expressed in meters and seconds, respectively. Determine (a) the distance between the car and the girl when t = 2 s, (b) the distance the car traveled in the interval from t = 0 to t = 2 s, (c) the speed and direction of the car's velocity at t = 2 s, (d) the magnitude of the car's acceleration at t = 2 s.

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Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be created or destroyed — only transformed.