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Two cars, A and B, start side by side and accelerate from rest. The figure shows the graphs of their velocity functions.(a) Which car is ahead after one minute? Explain.(b) What is the meaning of the area of the shaded region?(c) Which car is ahead after two minutes? Explain.(d) Estimate the time at which the cars are again side by side.

a) car $A$ is aheadb) the distance from car $B$ to car $A$ after 1 minutec) car $A$ still ahead, but $B$ is gainingd) Estimate of 2.3NO DEFINTTE ANSWER

Calculus 2 / BC

Chapter 6

Applications of Integration

Section 1

Areas Between Curves

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Two cars _ Aand B> star…

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Automobile Velocity Two ca…

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Distance Traveled Cars $A$…

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Velocity-time graphs of tw…

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Graphs of velocity $\righ…

03:07

Two cars travel in the sam…

02:38

A car moves along a straig…

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Two vehicles start out tra…

01:01

Two cars, side by side, st…

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Distance between Cars Cars…

01:07

The accompanying figure sh…

goes a part? A. Since car has had a higher velocity for the first minute, car is in the lead, okay? And in areas under velocity, curves for part B is the total distance of cars traveled. Eso the meaning of the of this particular shaded region Because it's between A and B. It is the distance that a is ahead of B if we calculate the area. So the meaning of that shaded regions the distance between A and B and with the knowledge that a is ahead. A part of C says which car is ahead after two minutes. Poof! It's getting closer, I would say is still in lean. Um, really, you're just comparing the, uh, uh, the areas between So the first amount of area looks a little bit larger than the area between one minute and two minutes, because every between woman and two minutes is the distance that B has gained. Okay? And then so Part D just has to estimate when they're side by Assad. Ah, it's without having the actual formulas. It's gonna be a little bit past two, but not much so if I had to estimate just kind of counting squares? Um, yeah. I don't, uh I probably around 2.2 somewhere between 2.2 and 2.4. Really? You can't, um, conclude this without actual functions, but that's around the time that that the area, after one minute will equal the area before One minute, okay?

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