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The speed of the roller coaster will be limited by various sources of resistance such as that of its wheels on the rails and its passage through the air. If we ignore these we can get an upper bound on the vehicle's speed. You have probably seen the equation that relates final velocity to initial velocity, acceleration and displacement:

v2 = u2 + 2as

where v is initial velocity, u is initial velocity, a is acceleration and s is displacement. In this case acceleration is g, gravitational acceleration, and u is zero.

We have : v2 = 2 . 9.80665 m.sec-2 . 100 m = 1961.33 m2.sec-2

Then v = sqrt (1961.33) m.sec-1 ~= 4.43 m.sec-1

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Q: What is its speed at point B if a roller coaster car started from point A at a height of 100 meter?
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