Final answer:
The slope of a curve at a point is equal to the slope of a straight line tangent to the curve at that point. In this case, there is no place on the curve where the tangent line has a slope of 2.
Step-by-step explanation:
The slope of a curve at a point is equal to the slope of a straight line tangent to the curve at that point.
In this case, the slope of the curve is given as 2. To find where the tangent line intersects the curve, we need to determine the position of the curve at two different times.
Let's assume the position of the curve at t = 19 s is 1300 m and the position at t = 32 s is 3120 m. These will be the endpoints of the tangent line.
Using the endpoints, we can calculate the slope of the line using the formula: slope = (change in y) / (change in x) = (3120 - 1300) / (32 - 19) = 1820 / 13 ≈ 140.
The tangent line intersects the curve at a slope of 2, which is not equal to 140, so there is no place on the curve where the tangent line has a slope of 2.