Im confused on how to do part b, do i just find t when x = 0, then plug in the value of t into velocity and acclereation equation?

forget problem 1, i figured it out

integral of acceleration from 40 to 100 is = 18mm/s

tat doesnt give u the correct k value, the correct k is .09

my bad, not with respect to time anymore


with accel equations with position instead of time

use a * dx = v *dv
dx is from 40 to 100
dv is from 0 to 18
you'll get .09 exactly

(b) The first derivative with respect to time is a mathematical method to find the equation for velocity.
TO solve when x=0 you will end up with a polynomial of highest order two after taking the first derivative. At this point you want to resort to either the FOIL factorization method or make quick use of the quadratic formula to find the root(s).

The acceleration is merely the same process, except with the second order derivative.

i did it the other way where instead of using boundaries in the integral, I just integrated both sides and get a constant and i solved for C then after u get C u get k.

is there situations where I should be using ur method instead? If so, can u give an example?

i'm not sure exactly what you did
it's possible you actually got lucky with the boundaries

u know how when u integrate without limits, u get a constant? so i did it that way, to get a constant. then i used the two boundaries to solve for the constant, C.

From there ill get k