The area under the velocity time graph gives the distance covered
a. Please find attached the velocity time, v-t, graph for the first car
b. The displacement of the car is 150 m
c. Please find attached the v-t graph for the second car
d. The cars velocity is given by the ratio of the given distance to the given time
The reason the above values are correct are as follows;
The given parameter are;
The initial velocity of the car, v₀ = 0 m/s
The final velocity of the car, v₁ = 25 m/s
The direction of travel of the car = Western direction
a. The table of values for drawing the velocity time graph of the car's motion are as follows;
[tex]The \ acceleration \ of \ the \ car, \ a = \dfrac{v_1 - v_0}{\Delta t}[/tex]
Therefore, we have;
[tex]The \ acceleration \ of \ the \ car, \ a = \dfrac{25 - 0}{12} = 12.08\overline 3[/tex]
The velocity, v at time t is given as follows;
v = u + a·t
Which gives
[tex]\begin{array}{|c|cc|}\mathbf{t}&&\mathbf{v}\\1&&2.09\\2&&4.17\\3&&6.25\\4&&8.33\\5&&10.42\\6&&12.50\\7&&14.58\\8&&16.67\\9&&18.75\\10&&20.83\\11&&22.92\\12&&25.00\end{array}\right][/tex]
Using the above table, the velocity time, v-t, graph can be constructed
b. The displacement can be found from the velocity time graph by finding the area under the graph as follows;
The area of the graph is the area of a triangle of base length = 12, and height = 25
Therefore, the triangular area of the velocity time graph, A, is given as follows;
[tex]A = \dfrac{1}{2} \times 12 \times 25 = 150[/tex]
The triangular area of the velocity time graph, A = 150 = The displacement of the car
The displacement of the car, d = 150 m
c. The distance traveled by the second car = the distance traveled by the first car = 150 m
The time the second car uses to travel the distance, t = The same as the first car = 12 s
Therefore;
[tex]The \ velocity \ of \ the \ second \ car, \ v = \dfrac{Displacement}{Time} = \dfrac{150 \ m}{12 \ s} = 12.5 \ m/s[/tex]
Given that the velocity is constant, we have;
[tex]\begin{array}{|c|cc|}\mathbf{t}&&\mathbf{v}\\1&&5\\2&&5\\3&&5\\4&&5\\5&&5\\6&&5\\7&&5\\8&&5\\9&&5\\10&&5\\11&&5\\12&&5\end{array}\right][/tex]
With the above table, the graph of the car can be plotted as follows;
The v—t graph for the car is plotted using the data in the above table using MS Excel
d. The new car's velocity is found from the given the ratio of total distance to total time, with the following formula;
[tex]The \ velocity \ of \ the \ second \ car, \ v = \dfrac{Total \ displacement}{Total \ Time \ Taken}[/tex]
Learn more about velocity time graph here:
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