Question

Determine the displacement of the vehicle between the interval t = 0 s to 2 s.

Answer 1

In order to determine the displacement of the vehicle, first calculate the acceleration, by using the following expression:

`a=(v_2-v_1)/(t_2-t_1)`

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:

`a=(5(m)/(s)-0(m)/(s))/(1s-0s)=5(m)/(s^2)`

Now, to calculate the displacement, you can use the following expression:

`x=v_ot+(1)/(2)at^2`

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:

`\begin{gathered} x=(0(m)/(s))(2s)+(1)/(2)(5(m)/(s^2))(2s)^2 \\ x=10m \end{gathered}`

Hence, the displacement of the vehicle in the given time interval is 10m