Final answer:
To estimate the slope of the tangent line at a point, calculate the slope of two secant lines passing through that point and adjacent points on the curve, then average these slopes. Use the slope formula to find the slope of each secant line.
Step-by-step explanation:
To estimate the slope of the tangent line at a given point P(15, 1040) by averaging the slopes of two adjacent secant lines, you can follow these steps:
- Identify two points close to P(15, 1040) on either side along the curve. Let's call these points Q and R.
- Calculate the slope of the secant line passing through points P and Q, and then do the same for the secant line passing through points P and R.
- Average these two slopes to get an approximation for the slope of the tangent line at P.
For example, if the endpoints of the tangent line correspond to a position of 1300 m at time 19 s and a position of 3120 m at time 32 s, plug these into the slope formula:
Slope, v = (Final position - Initial position) / (Final time - Initial time)
In this case:
v = (3120 m - 1300 m) / (32 s - 19 s) = 1820 m / 13 s = 140 m/s