Question

Integrals of a velocity function:
I'm given a piecewise function of v(t), and I need to find a piece-wise function for s(t), where s is the position function.

Answer 1

Here is the piecewise function for velocity.

Answer 2

@Vocaloid Are you able to help love?

Answer 3

As you can see, they're all constants. So I thought to find the position functions of each, i'd just have to integrate them.

So they all become 30t, 40t, and 36t. But for the 2nd and 3rd functions, I'm supposed to add a constant, and I can't figure out why.

Answer 4

Hm.

Answer 5

I might be missing some context here.
Here's a copy-paste of the actual question:

The following function describes the velocity of a car​ (in mi/hr) moving along a straight highway for a 44​-hr interval. Find the function that gives the displacement of the car over the interval​ [0,t], where 0 <= t <= 4

Answer 6

This is just a guess based on my intuition: for the first function you are considering the initial displacement during the 0 to 1.5s interval

Perhaps they want you to add the previous displacement to the next time interval as a constant, so the distance is Airulative

Answer 7

yeah I actually just realized that, I was thinking of each interval as if they all started from 0.

Answer 8

Okay recognizing that problem should help me figure it out

Answer 9

No problem, I am not 100% sure but I think that's a good place to start

Answer 10

Alright I got it. Since I'm just finding the area under the lines, i did some geometry
For the 2nd interval, I had to do 40t subtract whatever the area of that red bar is.

And I can do the same for the 3rd interval.