Final answer:
To find the slope of a curve without calculating the derivative, choose two widely separated points on the curve and calculate the rise and run between these points. Then, divide the rise by the run to find the slope.
Step-by-step explanation:
To find the slope of a curve without calculating the derivative, we can approximate it using two points on the curve. Choose two widely separated points on the curve. In this case, we can use the points labeled on the graph: (6.4 s, 2000 m) and (0.50 s, 525 m).
Next, calculate the rise and run between these two points. The rise is the difference in the y-values of the two points, and the run is the difference in the x-values. In this case, the rise is 2000 m - 525 m = 1475 m, and the run is 6.4 s - 0.50 s = 5.9 s.
Finally, calculate the slope by dividing the rise by the run: slope = rise / run = 1475 m / 5.9 s ≈ 250.0 m/s.