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# Independent of what variable?

d=Vi t 1/2 at^2 is independent of what variable?

(1)a
(2)Vi
(3)Vf
(4)d

### 1 Answer by Expert Tutors

Arturo O. | Experienced College Instructor for Physics TutoringExperienced College Instructor for Physi...
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I think you meant so say

d(t) = vit + (1/2)at2,

which is distance traveled at constant acceleration a, with initial speed vi, starting from d = 0.

The quantities vi and a are constants.  The independent variable is time t.  Note that d(t) does not depend on final speed vf.

I understand that "t" is the independent variable. However, i don't think that's what The question is asking as it Is not one of the choices. The question is asking what variable that equation is independent of.
therefore, would it make sense to say that the answer is choice Vf because it does not appear in the equation at all? If it helps, this is how one would get to the equation above:
you would have to combine these two equations to eliminate Vf and get the equation in the question.
delta d = 1/2 (Vi +Vf) delta t
AND
Vf = Vi t a delta t
I understand that "t" is the independent variable. However, that's not what the question is asking. The question is asking what variable that equation is independent of.
therefore, would it make sense to say that the answer is choice Vf because it does not appear in the equation at all? If it helps, this is how one would get to the equation above:
you would have to combine these two equations to eliminate Vf and get the equation in the question.
delta d = 1/2 (Vi +Vf) delta t
AND
Vf = Vi t a delta t
It is correct to say that d(t) does not depend on vf, so the answer from the list is (3).
But I should also clarify that technically, vf is not a a variable in this problem.  It is a constant.