# Average acceleration when more than two different velocities occur [closed]

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?

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?

• So I only have to vectorally subtract the 10m/s and the 5m/s? Commented Sep 4, 2014 at 22:30
• I'll leave that for you to decide.
– BMS
Commented Sep 4, 2014 at 22:30
• 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 Commented Sep 4, 2014 at 22:36
• True, because for average velocity you don't subtract displacements; you subtract positions.
– BMS
Commented Sep 4, 2014 at 22:37
• There we go, that was it, thankyou so much for helping me! Now I get what's going on. Commented Sep 4, 2014 at 22:40