Answer:
1. r = 5 m 2. a = 25.6 m/s²
Step-by-step explanation:
The relation between the velocity, the radius of path and the acceleration on the circular path is given by :
![a=\dfrac{v^2}{r}](https://tex.z-dn.net/?f=a%3D%5Cdfrac%7Bv%5E2%7D%7Br%7D)
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=\dfrac{v^2}{a}\\\\r=\dfrac{(14)^2}{39.2}\\\\r=5\ m](https://tex.z-dn.net/?f=r%3D%5Cdfrac%7Bv%5E2%7D%7Ba%7D%5C%5C%5C%5Cr%3D%5Cdfrac%7B%2814%29%5E2%7D%7B39.2%7D%5C%5C%5C%5Cr%3D5%5C%20m)
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=\dfrac{8^2}{2.5}\\\\a=25.6\ m/s^2](https://tex.z-dn.net/?f=a%3D%5Cdfrac%7B8%5E2%7D%7B2.5%7D%5C%5C%5C%5Ca%3D25.6%5C%20m%2Fs%5E2)
Hence, this is the required solution.