Need help with non-uniform circular motion question

[plane]

this is the question:

i have no idea how to start this, my initial thougts were to plug things into kinematic equations to get the acceleration but i really don't know. i know tangental acceleration is the derivative of the velocity equasion, but i just don't know how to get the velocity equasion. do i plug numbers into the formula "vf= vi + at" ?

if so, then what would my acceleration be in that formula? if not, what other formula can i use?
thanks for the help.

 

[Pythagorean]

this is the question:

i have no idea how to start this, my initial thougts were to plug things into kinematic equations to get the acceleration but i really don't know. i know tangental acceleration is the derivative of the velocity equasion, but i just don't know how to get the velocity equasion. do i plug numbers into the formula "vf= vi + at" ?

if so, then what would my acceleration be in that formula? if not, what other formula can i use?
thanks for the help.

Think of a wheel with a stud on it, spinning around. Watch the stud as it spins around on the surface of the weel.

If you laid the path of that stud out flat, and imagine the stud traveling that fast in a straight line, that would be the tangential component of motion (motion being velocity and position) (question b in your problem).

The equation you gave includes a's tangential component. That is, it tell you how fast that stude accelerated around the point.

The centripedal acceleration uses a different formula that has something to do with the radius. If you drew a chalk line on the sidewall of the tire, from the center of the wheel out to the studs, the centripedal velocity would be how fast that whole line spun around the midpoint, how that velocity changes with time is the angular acceleration.

See what you can do with that, and show us your work if you need more help.