Question

50 points!

Marc left his house to drive to work. He slowly pulls out of his driveway at a constant speed, and then his speed increases steadily until he reaches the speed limit. He uses cruise control to drive the speed limit until he comes upon some traffic. He then slows down to a new constant speed. When he gets near his office, his speed steadily decreases until he comes to a stop right in front of his office building.

Which graph represents Marc’s drive to work?

Answer 1

Answer: the first one

Explanation:

Answer 2

The right graph is the first one (figure attached).

Note that in a Speed vs Time graph, the constant speed is represented by a line with slope=0 (for example, segment 1), when the speed increases the slope is positive (for example, segment 2) and when the speed decreases the slope is negative (for example, segment 4).

Now, if we want to prove this, let’s read again the problem, dividing each section of the path Marc drove to his work (see figure attached):

1. He slowly pulls out of his driveway at a constant speed

2. and then his speed increases steadily

3. until he reaches the speed limit. He uses cruise control to drive the speed limit (he drives at constant speed)

4. until he comes upon some traffic (usually if you find some traffic you have to derease your spped)

5. He then slows down to a new constant speed.

6. When he gets near his office, his speed steadily decreases until he comes to a stop right in front of his office building (at this point the speed is zero)