A roller coaster car travels through a loop in 3.1 s with a centripetal acceleration of 26 m/s2. What is the radius of the roller coaster loop?

If the car completes one loop in 3.1 s, its speed is related to the loop radius by v = 2πr/T. Using centripetal acceleration a = v²/r gives r = aT²/(4π²). Substituting a = 26 m/s² and T = 3.1 s gives r ≈ (26 × 3.1²)/(4π²) ≈ 6.3 m, so the radius is 6.3 m.

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