In order to determine the displacement of the vehicle, first calculate the acceleration, by using the following expression:
[tex]a=\frac{v_2-v_1}{t_2-t_1}[/tex]
where t1, t2, v1 and v2 are values of time and velocity you can determine from the graph. For instance:
v1 = 0m/s
v2 =5m/s
t1 = 0s
t2 = 1s
By replacing the previous values of the parameters into the formula for a you get:
[tex]a=\frac{5\frac{m}{s}-0\frac{m}{s}}{1s-0s}=5\frac{m}{s^2}[/tex]
Now, to calculate the displacement, you can use the following expression:
[tex]x=v_ot+\frac{1}{2}at^2[/tex]
Between time t=0s and t=2s, you have vo = 0m/s.
Use a=5m/s^2 and t=2s and simplify into the expression for the displacement x:
[tex]\begin{gathered} x=(0\frac{m}{s})(2s)+\frac{1}{2}(5\frac{m}{s^2})(2s)^2 \\ x=10m \end{gathered}[/tex]
Hence, the displacement of the vehicle in the given time interval is 10m
