Question

Calculus 3 (magnitude of vector)

The scrambler machine at the amusement park has big arms with 12ft and small arms with 8ft. which has rotation speed of 5 secs per lap for big arm and 3 secs per lap for small arm. The big arm rotates clockwise and small arm rotates counterclockwise. After doubling the rotation speed. What is acceleration of the cart?

I think I should get derivative of first value to get acceleration because this question asking about acceleration from speed. but not certain. Should I get v(t) and convert into a(t) by getting a derivative of v(t)? I don't know how to use vector function to solve this problem here.

Answer 1

Yes,

By definition we know that acceleration is a derivative of the velocity with respect to time.

So, you first find the velocity vector in the form of v=ai + bj+ ck where a,b,c will be functions of time.

So, acceleration will be dv/dt.

Acceleration=(da/dt)i + (db/dt)j+ (dc/dt)k