Question

A car is moving southwest at a velocity of 10 meters per second. Five seconds later, it's going 40 meters per second. What was the car's average acceleration during this time?

Answer 1

If "during this time" refers to the 5 second interval mentioned above, then the average acceleration is

`\bar a=(v-v_0)/(t-t_0)=(40\,(\mathrm m)/(\mathrm s)-10\,(\mathrm m)/(\mathrm s))/(5\,\mathrm s-0\,\mathrm s)`

Notice that we took the start time to be the start of the 5 second interval and set that to
`t_0=0`. The starting velocity
`v_0` is the velocity measured at the start of the interval, and
`v` is the velocity measured at its end.

So the average velocity over these 5 seconds is

`\bar a=(30\,(\mathrm m)/(\mathrm s))/(5\,\mathrm s)=6\,(\mathrm m)/(\mathrm s^2)`