A student estimates that his daily commute to college...

A student estimates that his daily commute to college consists of 10 minutes driving at a speed of 30 mph to a divided highway, followed by 5 minutes in which he accelerates to 65 mph, followed by 15 minutes driving at 65 mph before slowing to exit and enter the parking lot. The figure shows his velocity in terms of time. v(t) miles per hour 70 50 30 10 0.1 1/6 0.2 1/4 0.3 0.4 0.5 t hours (a) What are the units of measure of height, width, and area of the region between the speed graph and the horizontal axis? height miles per hour width hours area miles (b) How far does the student drive on his commute from home before exiting to the parking lot? (Round your answer to one decimal place.) mi

Transcript

00:01 Okay, so for this question, we are given this graph.

00:07 We are told that it's a graph of velocity.

00:11 So this is going to be v of t after t hours.

00:30 And we are asked to find how far the student drives on his commute from home before exiting to the parking lot.

00:38 So you have correctly identified in the previous question.

00:42 That if we're looking for a number of miles, that's going to be the area underneath this curve.

00:50 So another way you could figure that out is the relationship between position and velocity.

00:56 Velocity is the derivative of position, which means that position is the integral of velocity.

01:13 So basically, if we knew what this function was, we could take the integral of it.

01:18 We don't.

01:19 But the graph is very nicely divided up for us into some geometric shapes that we can find the area of using just geometric formulas.

01:31 So if we think about this first square, for example, we can just use the area of a square formula to find that, right? so i'm going to label this area one.

01:46 So the area of square one here is just going to be base times height.

01:52 The base is one -sixth, and the height is 30.

01:59 So if we calculate that area, one -six times 30 is just going to be five.

02:07 So that area is going to be five miles.

02:15 And then we have another area here.

02:19 Let me get the straight line tool out because this one's a little trickier.

02:25 There we go.

02:27 So this one i would actually just treat as like a compound area of like a square and a triangle on top of it or a rectangle and triangle.

02:40 So i'm going to label the rectangle as two and the triangle as three.

02:45 So let's find the area of just this rectangle.

02:49 So that rectangle's base is going to be one fourth minus one sixth, which is going to be.

03:02 Let's see we might have to do some fraction math here let's get some common denominators oh and the height is just going to be 30 again so let's figure out what one -fourth minus one -sixth is a common denominator there could be 12 so that's going to be 3 twelfths minus 2 twelfths times 30 so that is going to be 112 times 30 divided by 12.

03:49 Let's see what that is...

Question

Please give Ace some feedback