Question

Directions: For a spinning amusement park ride, the velocity v in meters per second of a car moving around a curve with a radius r meters is given by the formula v= √ar, where a is the car’s acceleration in m/s2.

1. For safety reasons, a ride has a minimum acceleration of 39.2 m/s2. If the cars on the ride have a velocity of 14 m/s what is the smallest radius that any curve on the ride may have?

2. What is the acceleration of a car moving at 8m/s around a curve with a radius of 2.5m?

Answer 1

1. r = 5 m 2. a = 25.6 m/s²

Explanation:

The relation between the velocity, the radius of path and the acceleration on the circular path is given by :

`a=(v^2)/(r)`

1. Acceleration, a = 39.2 m/s²

Velocity of the car, v = 14 m/s

The radius of the path can be calculated using the above formula i.e.

`r=(v^2)/(a)\\\\r=((14)^2)/(39.2)\\\\r=5\ m`

2. Velocity of the car, v = 8 m/s

The radius of the path, r = 2.5 m

The acceleration of the car is given by :

`a=(8^2)/(2.5)\\\\a=25.6\ m/s^2`

Hence, this is the required solution.