Graphs of functions in context
About this video
A car drives away from its driveway at a constant speed, stops at a red light, then drives on at the same speed. Sal sketches distance against time (a straight rising line, a flat part, then another rising line with the same slope) and picks graph B, explaining why A and C do not fit.
You'll be able to
- sketch a distance-time graph from a story.
- explain that constant speed gives a straight line and stopping gives a flat section.
- explain why a vertical jump or a falling section does not match the story.
Key words
- constant speed
- Moving the same distance in each equal amount of time, shown as a straight line on a distance-time graph.
- slope
- How steep a line is; on a distance-time graph it shows speed.
- function of time
- A quantity, like distance, whose value depends on the time.
Transcript
- [Narrator] We're told that a car drives away from its driveway at a constant speed. Then they say after a stoplight, or after a stop at a red light, the car drives away again from the driveway at the same constant speed. Which graph best represents the car's distance from the driveway as a function of time?
So pause this video and have a go at that before we do it together. Okay, I actually just like to try to sketch it myself, and see if one of these seems pretty close to that. So if this is distance in the vertical axis, and then this is time, right over here. Time, this is distance.
Okay, drives away from its driveway at constant speed. So that means that the distance would be increasing at a constant rate, so a constant slope. So the distance would be increasing. So that would be that. That should be a straight line I tried to hand write.
After a stop at a red light. So time is going to pass, and we're not going to have any change in distance while we're on that red light. So we don't know how long it is, but it's going to be a flat point, or a flat part of this graph. And then once the light turns green again, the car drives again away from the driveway at the same constant speed.
So the distance is going to be increasing again. So we should see a graph that looks something like that. And that looks like choice B. I like choice B. But let's think about what happens at choice A. Here you drive away, you have a stoplight, and then this looks like you drive back to the driveway.
That's not what's going on. Here, you drive away, and then you're going infinitely fast. Your B going faster than the speed of light? Physics don't even allow, you teleport, it looks like what's happening here. And then you drive away at a constant speed. So I definitely don't like A or C.
Now in the real world, it's hard to just go from a stop to a true constant speed. There'd be some acceleration, so this would be a curved a little bit when you go from start to stop, or from stop to start at a constant speed. But for sake of simplicity, B is pretty good.
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