To find the tangents to a curve, determine the endpoints corresponding to specific time values and calculate the slope of the tangent line using those points.
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 tangent line to a curve at t = 25 s, you need to determine the endpoints of the tangent line. These endpoints 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.