Question

The distance x of a runner from a fixed point is measured (in meters) at intervals of half a second. The data obtained is: t (seconds): 0, 0.5, 1, 1.5, 2, 2.5 x (meters): 0, 4, 9, 14, 20, 26. Using a central difference, what is the approximate velocity of the runner at t=1s?

Answer 1

The approximate velocity of the runner at t=1s is 9 m/s.

Step-by-step explanation:

To calculate the approximate velocity of the runner at t=1s using central difference, we need to find the difference in distances at adjacent intervals and divide by the difference in time.

Let's find the difference in distances first:

Δx = x2 - x0

Δx = 9 - 0 = 9 meters

The difference in time is 1s - 0s = 1s.

Now, we can calculate the velocity:

velocity = Δx / Δt

velocity = 9 meters / 1s = 9 m/s