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Potential energy is calcualted as mgh. So the highest potential energy is found at the highest point of the roller coster  (which is usually the first drop) so highest point is depicted in this image of the Texas Giant.

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The highest kinetic energy is at the lowest point of the first drop as ALL the potential energy is converted into kinetic energy. This picture is a depiction of this concept as it depicts the lowest point of the roller coaster after the first drop. Kinetic energy is also described as 1/2mv(squared), and the velocity is the greatest at the bottom of the roller coaster therefore the KE is the highest.

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This depiction of the Batman represents centripetal acceleration because the roller coaster is moving in a uniform circular motion as it goes through the loop. Centripetal acceleration always points to the center of a circular path where the only force acting upon it is centripetal force.  The centripetal force keeps the roller coaster moving in the circular motion while it's going through the loop.

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A pendulum is one the best representations of simple harmonic motion and in the picture of the Riddler, the ride swings back and forth like a pendulum in harmonic motion.

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When a object is in free fall there are no other forces acting on it except gravity (which accelerates at a rate of -9.8 m/s) In this video the riders are released from the top and fall with no other force acting upon them except gravity.

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In this image Kenneth is depicted moments before slamming down on a cylinder. Since Impulse is Force times Time,  when a person (in this image Kenneth) applies a force to the cylinder for a given amount of time, they are causing an impulse.

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Work is Force times Distance and as this roller coaster is moving upwards, it has a component of a force that is acting in the direction of motion which allows it to move upwards at a slope. That's why there is work being done on the roller coaster as it moves up.

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Since the superman is moving up and speeding up, it has a positive acceleration upwards.

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Anything that is moving downwards experiences the acceleration of gravity, which is negative 9.8. When the Mr. Freeze is moving down the slope, it is speeding up in the negative direction and has the force of gravity acting upon it, so it has a negative acceleration.

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When the roller coaster comes to a jolting stop, the people riding the roller coaster have a tendency to keep moving forward due to newton's first law of inertia. This law states that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. In this case the people keep moving forward and then are jolted back.