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
Acceleration is defined as:
$$$a=\frac{dv}{dt}$$$
where
$$v$$
is velocity and
$$t$$
is time.
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 plot’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:
$$$a=\frac{5m/s-1m/s}{9s-5s}=\frac{4m/s}{4s}=1\:m/s^2$$$
$$$1\:m/s^2$$$