The correct answer to the question “What is the magnitude of the displacement of the car from t=2.0 seconds to t = 4.0 seconds in the graph below?” wherein the graph “shows the velocity of a race car moving along a straight line as a function of time” is letter B or 20. m. Displacement is the area of curve bounded by time 2 seconds to 4 seconds and velocity of 20 m/s to 40 m/s.
To get the displacement, the formula that we have to use is this: ½ (4 seconds – 2 seconds) (40 m/s – 20 m/s). Now, using this formula, we can get the answer and it will show us that the displacement of car from t = 2.0 seconds to t = 4.0 seconds is 20m. Hope this answers the question.
Think about it logically - between 2 and 4 seconds, object is travelling between 20-40km/hr, ie an average of 30km/hr for 2 seconds, therefore answer has to be 60m. Also, mathematically, displacement is the area beneath the graph between t=2 to t=4, which is 60m.
The programmer clearly thought he was using a complete Cartesian plane, and that the first to the second interval was in the negative (third) quadrant. The correct answershouldbe 60 meters, but, assuming that the programmer is not totally incompetent, and intended the centre lines to be the zero on the x and y axis, then 20 meters would be correct. Unless the programmer is, in fact, a human being, in which case we may simply say; he made a boo boo. :)