Final answer:
To find the parametric equations for the tangent line to the curve, determine the slope of the curve at the given point and use the formula (change in y)/(change in x) to find the slope of the tangent line. The equation of the tangent line can be written as y = mx + b, where m is the slope and b is the y-intercept.
Step-by-step explanation:
To find the parametric equations for the tangent line to the curve, we need to determine the slope of the curve at the given point. In this case, the point is t = 25 s.
We are also given the endpoints of the tangent line, which correspond to a position of 1300 m at time 19 s and a position of 3120 m at time 32 s.
The slope of the curve at the given point is equal to the slope of the tangent line. We can find the slope by using the formula (change in y)/(change in x) and plugging in the coordinates of the endpoints. The equation of the tangent line can then be written as y = mx + b, where m is the slope and b is the y-intercept.