Final answer:
To find the equation of the secant line and tangent line, determine the endpoints of the tangent line and substitute them into the equation to solve for the slope. The equation of the secant line is y = mx + b, where m is the slope and b is the y-intercept. The equation of the tangent line is y = mx + b, where m is the slope and b is the y-intercept.
Step-by-step explanation:
To find the equation of the secant line and tangent line, we first need to determine the endpoints of the tangent line. In this case, the endpoints correspond to a position of 1300 m at time 19 s and a position of 3120 m at time 32 s.
Next, we substitute these endpoints into the equation to solve for the slope. The slope, denoted by v, is equal to the change in position divided by the change in time: (3120 m - 1300 m) / (32 s - 19 s) = 1820 m / 13 s = 140 m/s.
Therefore, the equation of the secant line through the points is y = mx + b, where m is the slope (140 m/s) and b is the y-intercept. For the equation of the tangent line, we substitute the given x-value (t = 25 s) into the equation: y = 140 m/s * 25 s + b = 3500 m + b.