Question

Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = 2t + sin(t) and v(0) = 4.

a: v(t) = t^2 + cos(t) + 3
b: v(t) = 2 + cos(t) + 1
c: v(t) = t^2 − cos(t) + 5
d: v(t) = t^2 + sin(t) + 4

Answer 1

take the integral of 2t+sin(t)

Answer 2

for your "C" value use the fact that v(0)=4, to determine what the "c" will be

Answer 3

okay the integral is: t^2-cos(t)

Answer 4

`\(\large\color{slate}{\displaystyle\int\limits_{~}^{~}2t+\sin(t)~dt}\)`
you can use my latex.

Answer 5

yes,

Answer 6

\(\large\color{slate}{\displaystyle\int\limits_{~}^{~}2t+\sin(t)~dt~=~t^2-\cos(t)+C}\)

Answer 7

I think i got it! is it B? :)

Answer 8

V(t)=2+cos(t)+1
V(0)=2+1+1
V(0)=4

Answer 9

and you know that \(\large\color{slate}{\displaystyle~v(\color{red}{0})=\color{blue}{4}}\),

saying that
\(\large\color{slate}{\displaystyle~(\color{red}{0})^2-\cos(\color{red}{0})+C=\color{blue}{4}}\)

Answer 10

the velocity function is an integral of acceleration

Answer 11

Ohh then c = 5

Answer 12

yes

Answer 13

and your answer is?

Answer 14

you can already deduce by the fact the we have the cos(y) since that is integral of sin(t), and that it is negative cos(t).

Answer 15

:)
c: v(t) = t^2 − cos(t) + 5 thank u!!!!!!!!!!!!!!!!!!!!!!!

Answer 16

I mean cos(t)

Answer 17

yes C is correct

Answer 18

\(\large\color{slate}{\displaystyle~v(t)=t^2-\cos(t)+5}\)

Answer 19

you welcome !

Answer 20

Ur so good!!!!!!!!!!!!!

Answer 21

that is debatable, but good that I had that impression.

Answer 22

yw, and I will definitely take the complement. tnx

Answer 23

I have another question, can u plz help me with it? :)