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Suppose a car travels at 5m/s north for 5 seconds, it then turn east and travel at 7m/s for 10 seconds, finally it turns north east and travel at 10 m/s for 20 seconds. What is the average acceleration over these 35 seconds?

I know acceleration average is the change in velocity over the change in time. If there was just two vectors for velocity, then I would subtract those two vectorally. However, I don't know how to find the average acceleration from 3 or more vectors. Do I just subtract these 3 vectors vectorally and divide that the result by 35 seconds?

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closed as off-topic by ACuriousMind, Brandon Enright, Ali, John Rennie, Danu Sep 5 '14 at 7:07

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Whenever you're confused about how to calculate some quantity, try going back to the definition.

Think carefully about what the definition of average acceleration is:

$$\vec a_\textrm{avg}\equiv\frac{\vec v_\textrm{final}-\vec v_\textrm{initial}}{\Delta t_\textrm{elapsed}}.$$

Which velocities does this equation depend on? Which velocities does it not depend on?

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  • $\begingroup$ So I only have to vectorally subtract the 10m/s and the 5m/s? $\endgroup$ – Loc Tran Sep 4 '14 at 22:30
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    $\begingroup$ I'll leave that for you to decide. $\endgroup$ – BMS Sep 4 '14 at 22:30
  • $\begingroup$ Say if I replaced the velocities with distances...5 meters north, 4 meters west, 10 meters northwest...and I want to find average velocity. I can't just do 10 meters minus 5 meters vectorally $\endgroup$ – Loc Tran Sep 4 '14 at 22:36
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    $\begingroup$ True, because for average velocity you don't subtract displacements; you subtract positions. $\endgroup$ – BMS Sep 4 '14 at 22:37
  • $\begingroup$ There we go, that was it, thankyou so much for helping me! Now I get what's going on. $\endgroup$ – Loc Tran Sep 4 '14 at 22:40

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