Explanation

For an experiment, my group created a photo finish where the marble and the car ended at the same time. Then, we found the velocity of the car, by measuring how long it took the car to travel 1m. We found it took the car 2.2s to travel 1m so using the formula velocity= position/ time. The velocity is 0.45 m/s. Then we timed how long it took for the race to happen, and we got 5.4s. Then using the position formula: position= velocity*time. We multiplied the velocity we got before (0.45 m\s) * 5.4s and got 2.43 m was the final position. We knew that at 5.4s, both objects had traveled at 2.43 m . 

So then, we used the velocity vs time graph. 

We knew the displacement was the area of the shape (triangle) formed form the time axis. So, the area is 1/2*base*height. So the base is 5.4s, and the height is  change in velocity. We knew that the area was 2.43m. So we divided 2.43 by 0.5*5.4, and got 0.9m\s. So that is the final velocity because we know the marble started at a velocity of 0m/s. Then with those two points, we made a velocity vs. time graph. On the same graph, we drew the line velocity (y)=0.45 m/s. We then found the slope of the line for the marble line, and that number was 0.16 (m\s^2). That is the acceleration of the marble.


Since the area of shapes formed is equal to the total change in position, we knew that the area of the rectangle (outlined by the blue line and the +x-axis) was equal to the triangle (outlined by the red line and the +x-axis). The two shapes overlapped to form a trapezoid (the dark gray area) which is equal to 3 triangles (the light gray ones). In the beginning, the marble does not travel as much as the car because it has an acceleration, but we realized that the two triangles formed (when taking the two areas combined, they do not overlap at all or the light gray triangles) are congruent. This helps analyze a graph with two different data sets on it. It is easier to break the graph into triangles or smaller shapes to help understand the two separate motions.