Question

velocity vs time graph
time (sec) displacement (m) velocity (m/s)
0 0 0
0.5 1.25 5
1 5 10
1.5 11.25 15
draw conclusions as to how the acceleration is related to the time for the data table.
a the acceleration is a constant.
b the acceleration is constantly decreasing.
c the acceleration is constantly increasing.
d the acceleration cannot be determined from this data.

Explanation:

Step1: Recall acceleration formula

Acceleration $a=\frac{\Delta v}{\Delta t}$, where $\Delta v$ is change in velocity and $\Delta t$ is change in time.

Step2: Calculate acceleration between 0 - 0.5 s

$\Delta v = 5 - 0=5$ m/s, $\Delta t=0.5 - 0 = 0.5$ s. So $a_1=\frac{5}{0.5}=10$ m/s².

Step3: Calculate acceleration between 0.5 - 1 s

$\Delta v = 10 - 5 = 5$ m/s, $\Delta t=1 - 0.5 = 0.5$ s. So $a_2=\frac{5}{0.5}=10$ m/s².

Step4: Calculate acceleration between 1 - 1.5 s

$\Delta v = 15 - 10 = 5$ m/s, $\Delta t=1.5 - 1 = 0.5$ s. So $a_3=\frac{5}{0.5}=10$ m/s².

Answer:

A. The acceleration is a constant.