An object's velocity after t seconds is v(t) = 40

An object's velocity after t seconds is v(t) = 40 - 2t feet per second. (a) How many seconds does it take for the object to come to a stop (velocity = 0)? seconds (b) How far does the car travel during that time? feet (c) How many seconds does it take the car to travel half the distance in part (b)? seconds

Transcript

00:01 As we look at this velocity equation where we have 40 minus 2t, they kind of give it away on what to do in part a because they say if the velocity equals zero.

00:13 So if you set up the problem the way they tell you, all you have to do is add 2t to the right side and then divide both sides by 2 to see that the time it takes until the velocity gets to 0 would be 20 seconds.

00:27 Which you need in order to answer part b because they say, well, how am i? does it are traveled during that time well if you think about this being the velocity and that the i mean i write p for position that the derivative of position gives you velocity um so using that i'm just thinking out loud about how if i had 40 t the derivative of 40t would give me 40 so this would be like my position and then uh t squared because the derivative of t squared if you'd follow the power gives me 2t.

01:04 Now, i'm also going to go ahead and put that its starting position is at zero.

01:11 And the reason for that is because it doesn't really matter where you start, because all it's asking you for is the distance traveled.

01:20 So i'm going to make that start be zero.

01:24 So all i have to do now is figure out what the ending would be.

01:27 So plug in 40 and for t, sorry, 20 in for t.

01:35 And i think you could do this in your head but i'm going to use a calculator.

01:38 So if it's 40 times 20 would be 800 and 20 times 20, so 20 squared would be 400.

01:47 So it ends at 400.

01:51 So how much, how far did it go? it went 400.

01:56 I forgot what the units were feet.

02:00 It gets 400 minus zero.

02:06 And so now we're ready for part c.

02:08 How many seconds does it take for the car to travel half the distance? okay, so this is kind of a complicated thing because what you want to do is set the position which would be this 40t minus t squared equal to 200 half the distance, right? so what i would do, it's just a me thing, is because it's a quadratic, i would say it equal to zero.

02:32 So i would add t squared to the right side, subtract 40t and you have plus 200.

02:38 And now i have to think about if this is factorable, do we have factors of 200? the add to be 40, 200 divided by 25 is 8...

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