## Velocity Plots

An electron's motion is tracked and plotted in the shown diagram. What is the electron's acceleration between the 5 and 9 second data points in m/s^2?

##
__
__**Hint**

**Hint**

Acceleration is defined as:

$$$a=\frac{dv}{dt}$$$

where
$$v$$
is velocity and
$$t$$
is time.

##
__
__**Hint 2**

**Hint 2**

$$$a=\frac{dv}{dt}=\frac{\Delta v}{\Delta t}=\frac{v_{final}-v_{initial}}{t_{final}-t_{initial}}$$$

Acceleration is defined as:

$$$a=\frac{dv}{dt}=\frac{\Delta v}{\Delta t}=\frac{v_{final}-v_{initial}}{t_{final}-t_{initial}}$$$

where
$$v$$
is velocity and
$$t$$
is time.

The plotâ€™s x-axis is time and y-axis is velocity. Looking at the graph to find the corresponding velocity values associated with 5 and 9 second observation points:

Therefore,
$$v_{final}=5\:m/s$$
,
$$v_{initial}=1\:m/s$$
,
$$t_{final}=9\:s$$
, and
$$t_{initial}=5\:s$$
. Plugging these values into the acceleration equation:

$$$a=\frac{5m/s-1m/s}{9s-5s}=\frac{4m/s}{4s}=1\:m/s^2$$$

$$$1\:m/s^2$$$