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

$\bar a=\dfrac{v-v_0}{t-t_0}=\dfrac{40\,\frac{\mathrm m}{\mathrm s}-10\,\frac{\mathrm m}{\mathrm s}}{5\,\mathrm s-0\,\mathrm s}$

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

$\bar a=\dfrac{30\,\frac{\mathrm m}{\mathrm s}}{5\,\mathrm s}=6\,\dfrac{\mathrm m}{\mathrm s^2}$