Question

The position of an object changes with time according to the expression x(t) = 5t62 = 3t - 1. What is the position of the object when its velocity is 11 m/s?

Answer 1

Take the derivative of x(t) with respect to t to find a function v(t). Set that equal to 11, solve for t, then put that in to x(t) and compute x.

Answer 2

Do you mean x(t) = 5t^2 +3t -1?

What you wrote makes no sense.

If you meant what I wrote, the velocity at time t is
V = x'(t) = 10 t + 3

When x'(t) = 11,
11 = 10 t + 3
10 t = 8

t = 0.8

use x(t) to compute x at that time