A car going at 30 ft / sec decelerates at a constant 5 ft /...

A car going at $30 \mathrm{ft} /$ sec decelerates at a constant $5 \mathrm{ft} / \mathrm{sec}^{2}$ (a) Draw up a table showing the velocity of the car every half second. When does the car come to rest? (b) Using your table, find left and right sums which estimate the total distance traveled before the car comes to rest. Which is an overestimate, and which is an underestimate? (c) Sketch a graph of velocity against time. On the graph, show an area representing the distance traveled before the car comes to rest. Use the graph to calculate this distance. (d) Now find a formula for the velocity of the car as a function of time, and then find the total distance traveled by antidifferentiation. What is the relationship between your answer to parts (c) and (d) and your estimates in part (b)?

Transcript

00:01 So they want you to start with the making a table of values.

00:06 And for every one second, the car is decelerating.

00:15 So if i made a formula for velocity, i guess if i'm going to call it t, i better call this t as well.

00:24 So we're going 30 feet per second and then decelerating by 5, so 25, 23, i take it.

00:33 Takes me to 15 and then four seconds takes me to 10, five seconds takes me to five and then six seconds takes me to velocity of zero.

00:46 So i think that's all they want you to do.

00:49 Oh wait, they want every half second so i better imagine for a second i gave myself more room.

00:55 So at 0 .5 that order pair would be 27 .5 so i should have included that there.

01:05 So 1 .5 would be 22 .5.

01:09 So that would go there.

01:12 2 .5 would have been 17 .5.

01:18 And then 3 .5.

01:21 So it helps to read the direction.

01:23 Sorry, i didn't fit this in properly.

01:26 And then i'm really running out of room.

01:30 So i'll just keep going down 4 .5, 7 .5.

01:33 And that 5 .5 gives me 2 .5.

01:40 So those values go there and there if i was doing this properly.

01:45 So in part b, we can find the left and right sums for the total distance traveled.

01:54 Now, because velocity is decreasing, sorry, velocity is negative.

02:01 Well, i should say it that way.

02:03 Velocity is decreasing because it's going down but velocity is positive is why the left sum i just draw a picture real quick i think it'll make sense of your decreasing the left sum will be an over estimate is an over approximation and the right sum is an under so what i would do is using the table the values i came up with each one of these widths is 0 .5 so let me do the left sum is about 0 .5 for each width and then i just need to add together those numbers of 30 plus 27 .5 plus 25 plus 22 .5 and i'm just going to put dot dot dot all the way down until you get to 2 .5 because you want to ignore the right number there.

03:00 So i get an answer i'm using calculator.

03:03 5 parentheses.

03:17 Close my parentheses and i got an answer of 97 .5...

Question

Please give Ace some feedback