Problem: If velocity increases linearly from 6 meters per second to 66.45 meters per second in 4.65 seconds, then on the average, by how many meters per second does velocity increase per second?
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Solution: Velocity increases by ( 66.45 - 6) meters per second = 60.45 meters per second in 4.65 seconds. Per second, this is an increase of 60.45/ 4.65 meters per second, or 13 meters per second per second.
Generalized Response: The change in velocity is the difference `dv = vf - v0 between the initial and final velocities. The rate at which velocity changes is the velocity difference divided by the time interval: rate of velocity change = `dv / `dt = (vf - v0) / `dt.
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Figure description:
The figure below shows (blue lines) how the rate a at which velocity increases is obtained from `dv and `dt. This relationship is just part of the triangle relating a, `dv and `dt.
The figure also shows how `dv is obtained in the obvious way from v0 and vf: `dv is just the difference vf - v0 between the velocities.
Note that the full relationship a = `dv / `dt = (vf - v0) / dt is given. You should understand what this relationship tells you: that acceleration is the rate `dv / `dt at which velocity changes, and since `dv = vf - v0, this acceleration is (vf - v0) / `dt.
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