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[cursive marsh]

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[faint rose]

Note that v = dx/dt, a = dv/dt.
So, you need to solve a(t) = 1 in (a), integrate v(t) in the required interval in (b) (and take the absolute value if necessary), solve v(t) = 0 and integrate in (c) and integrate |v(t)| in (d).

[oblique hornet]

for a), dx/dt so that v goes to 0, then solve for 't' right?

[faint rose]

Yes. However, note that you are already given v(t), not x(t).

[oblique hornet]

ohhh

what topic/subject is this? ill go revise it

[faint rose]

Hm... Well, one-dimensional motion equations, I guess.

[oblique hornet]

right, thank you!

[faint rose]

You're welcome!

[oblique hornet]

ok i think i got it. do dv/dt = 1

because dv/dt = a
and a=1

dv/dt=1?

then solve for t

?

[faint rose]

Yes.

[oblique hornet]

im getting 2t= -1 but i dont think thats right

[faint rose]

Ah, sorry, I forgot: we need the magnitude of acceleration, so |a| = |dv/dt|.

[oblique hornet]

right so 'v' is a vector value not a scalar value in this question?

idk how to find 'a' then lol

[faint rose]

Yeah, technically a one-dimensional vector.

Well, we have:
v(t) = 8 + 2t - t^2
a(t) = 2 - 2t
|a(t)| = |2 - 2t| = 2|t - 1|
We need |a(t)| = 1. So:
2|t - 1| = 1
Now you need to solve this equation. Of course, you only need the nonnegative values of t.

[oblique hornet]

t=1.5?

[faint rose]

Is that the only root?

[oblique hornet]

i think so

[faint rose]

Can you show how you did it?

[oblique hornet]

my bad

t=2

2(t-1)=1
(t-1)/2= 0.5
t=2

but it says values so i might be wrong

[faint rose]

You forgot the absolute value.

[oblique hornet]

isnt the t=2 the absolute value though as its non-negative?

i dont know how to find another t value

[faint rose]

We have:
2|t - 1| = 1
|t - 1| = 1/2
When we remove the absolute value, we place a ± on one of the sides.
t - 1 = ±1/2
t = 1 ± 1/2
So, we get two values: t = 1 - 1/2 = 1/2 and t = 1 + 1/2 = 3/2.

[oblique hornet]

ohhh right

thanks for all the help

[faint rose]

You're welcome! Try the others now, they are a bit trickier.

[oblique hornet]

b)

or am i way off

[faint rose]

Well... Notation kinda sucks, to be honest 😅

[oblique hornet]

agreed

[faint rose]

You found the indefinite integral correctly, though.

Let me show.

Like this.

[oblique hornet]

oh right i get it

its way more simpler when you write it lol

i need to work on my notation

[oblique hornet]

for c)

80/3 is the answer i got (its kind of hard to read)

[faint rose]

Yeah, seems good.

[oblique hornet]

this is what part c is asking for right?

[faint rose]

If you meant part (d), then yes.

[oblique hornet]

+close