Question

A particle moves along the x-axis with a position function x(t).




Which position function x(t) is modeled by a velocity function of v(t) = x'(t) = -2 - 2t and an acceleration function of a(t) = v'(t) = -2?

Answer 1

x(t) will be the integral of x'(t)
in this case
x(t) = - 2t - t^2 (+ c )
where c is an unknown constant.

Answer 2

@phi would it be x(t)=6-2t-t^2

Answer 3

that will work. as a test, take the derivative:
x' = 0 -2 -2t = -2 - 2t which matches what they told you.

Answer 4

thanks!

Answer 5

yw