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The velocity graph of a car accelerating from rest to a speed of 120 km/h over a period of 30 seconds is shown. Estimate the distance traveled during this period.

.7056 kilometers were traveled.

00:28

Frank L.

01:06

Amrita B.

Calculus 1 / AB

Chapter 5

Integrals

Section 1

Areas and Distances

Integration

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

00:47

14.The velocity graph of a…

05:12

The $v-t$ graph for the mo…

06:25

A car accelerates smoothly…

01:39

Velocity The graph shows t…

03:12

The velocity of a car is p…

0:00

The velocity graph of an a…

00:57

06:03

The changing velocity of a…

07:17

03:03

Deceleration A car slows d…

to graph of a car accelerating from 0 to 120 kilometers per hour, and it's doing it in 30 seconds. And so the question is, how far has the card traveled in these 30 seconds. So if you have speed and you integrate it with respect to time, then what you're gonna have is distance. Okay, So all we have to do is figure out what's the integral of dysfunction. But we're just estimating. So the integral is always the area under the curve. So all we gotta do is figure out what the area is, but conveniently it's on graph paper. So all I have to do is count How many squares air in here? All right, let's start at the bottom. 12345 6789 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 whole ones. Now I'm just gonna start estimating 19.8 20.3 uh, 20.3. 21.2. 21.7. 22.6. 23. 23.8. 24. 24 point eight. 25 point a 25.7. So I have 25.7 boxes times. What does each box represent? Well, it's 20 kilometers per hour. And since we got second here, I gotta go ahead and switch that right there. That's one hour times One hour is 3600 seconds times five seconds. So each box is 20 by five. So 100 units, except for we gotta convert here. So now just multiply them all out. We'll see what we get. 25.7 times. 20 times five divided by 3600 0.714 kilometers. Okay. Um, now, remember. Sorry. Remember that. I just drew this graph from plotting some points that I picked off the graph in the book. So use the graph in the book and estimate is the best you can, and you should get something around 0.7. You might get more, you might get less, but that should be about how much it iss

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