Final answer:
To find the equation of the tangent line to a curve at a given point, find the slope of the curve at that point and use the point-slope form of a line.
Step-by-step explanation:
The equation of the tangent line to the curve at the given point can be found using the slope of the curve at that point and the coordinates of the point. First, determine the slope of the curve at t = 25 s by finding the slope between 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, v, can be calculated as (3120 m - 1300 m) / (32 s - 19 s) = 182 m/s. Next, use the point-slope form of a line to write the equation of the tangent line. The equation is y - 1300 m = 182 m/s * (t - 19 s).