4) This question is asking us to select the graph the best describes the object's displacement as time passes by. In order to find the object's displacement we can take the integral of the given velocity-time graph. This also means our final answer's slope at any moment, should be equal to the velocity of the given graph at that moment.
A good way to go about this problem is to split the graph into two parts. Again, much like we did for the third problem, we will use blue for part 1and orange for part 2.
Looking solely at part 1, we can see that the y-value(velocity) of the given graph is increasing at a constant rate, so that means our slope should increase at a constant rate. We can simply approximate a curve which matches the slope requirements.
The graph on the left is the given part 1. We were able to deduce that part 1 of our answer should look like the graph on the right. Thus, we can immediately get rid of answers A and D.
Now, we want to see how our graph would look for part 2. Since the object's speed is positive but slowing down(speed is approaching 0), we can tell that our answer should have a slope which is positive, but approaching zero. In order to satisfy these conditions, the graph of part 2 must be concave down.
From here we can clearly tell that the answer will be E. You can chose to use either method that we discussed. You can either look at the slope and use "dummy" values to make the problem easily manageable, or if you can quickly use concavity and slope to make a decent enough approximation.
Answer: E
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