Final answer:
The speed of a roller coaster at the top of a loop is determined using the centripetal acceleration formula and can be measured in m/s or km/h. Given a radius of curvature and a specified downward acceleration, the speed can be calculated. The mass of the roller coaster does not affect its speed when friction is negligible.
Step-by-step explanation:
The speed of a roller coaster could be measured in meters per second (m/s) or kilometers per hour (km/h). To determine the speed at the top of a loop when the radius of curvature is 15.0 m and the downward acceleration of the car is 1.50 g, we need to use the concept of centripetal acceleration, which is provided by the force of gravity in this case. The formula for centripetal acceleration (ac) is ac = v2 / r, where v is the linear speed and r is the radius of curvature.
Since the acceleration provided is 1.50 times that of gravity, we can express it as 1.50 g or 1.50 x 9.8 m/s2. By substituting ac with 1.50 g in the centripetal acceleration formula and solving for v, we can find the speed of the roller coaster at the top of the loop. Note that during the coaster's motion, if friction is negligible, the mass of the roller coaster does not affect its speed, and that speed can be determined at any point by considering the appropriate height (h) because, in a frictionless system, potential energy is converted into kinetic energy.