Question

If v=t^2-2t+1. Find s given that v=4 when t=1.

Answer 1

This makes no sense to me. What is "s"?

Answer 2

v cannot equal 4 when t = 1. When t = 1:
v = t^2 - 2t + 1 = 1 - 2 + 1 = 0.
Please check the problem statement.

Answer 3

"s" do you mean solution. Goodness, s is not a standard abbreviation.

v=4 when t=1 is not possible.

Now trying to decipher your cryptic problem statement.
is v velocity? Is s displacement? I can't imagine anyone assigning this without saying that. Even with that, it still makes no sense to me.

Answer 4

It is (somewhat) clearly a motion problem.

v(t) = t^2-2t+1
s(t) = 1/3 t^3 - t^2 + t + C
Now, knowing that v(1) = 4 does not help to find C.

Moreover, given the equation, it is clear that v(1)=0, not 4. So, let's assume that s(1) = 4. Then we have

1/3 - 1 + 1 + C = 4
C = 3 2/3 = 11/3

s(t) = 1/3 t^3 - t^2 + t + 11/3

If that is an incorrect interpretation of your garbled question, maybe you can fix it and the arrive at the solution.