Final answer:
To find the equation of the tangent line to the curve at t = 25 s, determine the endpoints of the tangent and solve for the slope.
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. To find the equation of the tangent line to the curve at t = 25 s, you need to determine the endpoints of the tangent. These correspond to a position of 1300 m at time 19 s and a position of 3120 m at time 32 s. Plug these endpoints into the equation to solve for the slope, v.