2. The figure below shows a graph of the position versus time for two cars, Car
ID: 1771728 • Letter: 2
Question
2. The figure below shows a graph of the position versus time for two cars, Car 1 and Car 2, that are going in the same direction on a straight road. Answer the questions below. Put your answers on this paper. x Position Car 2 Car 1 Car 2 time Car 1 t0 a. Place a letter S on the time axis on the above figure at any instant or instants when one car is passing the other. b. Place a letter V on the time axis on the above figure at any instant or instants when the two cars have approximately the same velocity c. At time t=0, the slower car is (circle one) 1 . Car ! 2.Car 2 . Over the period of time shown in the figure, Car 2 is: (circle one) 1. slowing down all the time. 2, speeding up all the time. 3. speeding up part of the time and slowing down part of the time.Explanation / Answer
a] Since the plot given above is a position vs time plot, therefore, when one car is passing the other, their position co-ordinates must be the same. So, the point of intersection of the two curves will be where they pass each other.
b] Velocity is rate of change of position with time. Hence velocity is the slope of the position vs time graph. This implies that the velocity should be same for the two cars where their slopes are the same. There is a point between the two intersections where the graphs become almost parallel. This is where the slopes (and hence velocity) are equal.
c] Initially, at t = 0s, Car 2 is just ahead of Car 1 and later in some time, Car 1 overtakes Car 2. Since the velocity of car 1 is constant (constant slope) therefore, the initial velocity at t = 0s is lower for Car 2 which implies that Car 2 is slower.
d] Slope of Car 2 is always positive and it itself increases over time. This means that the acceleration of Car 2 is positive. Therefore, it is speeding up all the time.
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