Having your space clean. have on close toed shoes. have your hair pulled back into a ponytail. keep ur work space clean. wear gloves and goggles. do not have on droopy clothes. follow the steps on the board and double check them.
Answer:
Part a)

Part b)

Part c)

Explanation:
Part a)
As we know that force on the passenger while moving in circle is given as

now variation in force is given as

here speed is constant
Part b)
Now if the variation in force is required such that r is constant then we will have

so we have

Part c)
As we know that time period of the circular motion is given as

so here if radius is constant then variation in time period is given as

If you are asking for a proof on having at least 3 dimensions in space, you can find the physical proof anywhere in your daily life activities. Just the fact that solids have volumes is a proof already that we live in a three-dimensional space. We can move forwards, backwards, sidewards and in all other directions possible.
When you go right into detail, the fundamental laws governing these proofs are very technical. They have differential equations to show as proof. It is too detailed to discuss here. The important things is that, these fundamental laws are what explains the science in our basic activities and natural phenomena:
*Gravitation and planetary motion
* Translation, rotation, magnetic field, forces
* Integrals of equations: