The object's acceleration is given by the expression: a(t) = 60t m/s^2. The distance it traveled after 10 seconds after starting from rest can be obtained by integrating the expression, a(t), twice in order to get the expression for the distance as a function of time.
The first integral of a(t) is the velocity, v(t), of the object which is then equal to: v(t) = 30t^2. The integral of v(t) is then distance, d(t), of the object which is then equal to: d(t) = 10t^3. With the distance equation available, we simply plug in t = 10 seconds into the equation. It is then determined that the object has traveled 10,000 m or 10 km after 10 seconds starting from rest.