A football player catches a ball at his goal line `(x =0)` at `t = 0`, and his motion is then graphed on the displacement `vs`. Time graph below.

(A) During which interval is the player accelerating away from his goal line?
(B) What is his velocity between points `B` and `C`?
(C ) describes his motion between points `C` and `D`.
(D) What is his velocity (magnitude and direction) during interval form `4s` to `6s`?

Explanation

(A) The player is accelerating during the interval `a` to `B`, since the graph is parabolic. This tells us that his velocity is increasing as he runs away form the goal line.
(B) The player's velocity between point `B` and `C` is the slope of the line between these two points.
slope =
`("rise")/("run") = (Deltax)/(Deltat) = (20m-10m)/(3s-2s) = 10m//s`
(C) During the interval from `C` to `D`, the time changes form `3s` to `4s`, but the player's position is not changing. He remains at rest at a distance of `20m` form the goal line, and thus his velocity is zero during this time interval. We could also say that since the slope of the line is zero, his velocity is zero, and the is at rest.
(D) The players' velocity between `4s` and `6s` is found by the slope of the line in that interval.
slope =
`("rise")/("run") = (Deltax)/(Deltat) = (0m-20m)/(6s-4s) =- 10m//s`
Since the slope is negative, the velocity is negative, which does not mean the player is followng down. A negative velocity means the player is runnning back toward his own, that is, the is moving backward compared to this motion in intervals `AB` and `BC`.