Given-the-acceleration-a-4sin2t-initial-velocity-v-0-2-and-the-initial-position-of-the-body-as-s-0-3-find-the-body-s-position-at-time-t-Hi-

Question Number 184832 by Mastermind last updated on 12/Jan/23

Given the acceleration

a = - 4 \sin 2 t, initial velocity

v (0) = 2, and the initial position

of the body as s (0) = - 3, find the

{body}^{'} s position at time t .

Hi

Commented by manolex last updated on 12/Jan/23

{d o n}^{'} t b e l i e v e, C H E C K

y o u a l c o h o l

s = 4 s i n 2 t - 3 s = s i n 2 t - 3

s (0) = - 3

v = 8 c o s 2 t v = 2 c o s 2 t

v (0) = - 2

a = - 16 s i n 2 t a = - 4 s i n 2 t

w r o n g o k

Answered by TheSupreme last updated on 12/Jan/23

v (t) = v (0) + \int_{0}^{t} a d t = 2 + 2 c o s (2 t)

s (t) = s (0) + \int v d t = - 3 + 2 t + s i n (2 t)

Commented by Mastermind last updated on 12/Jan/23

I got s = 4 \sin 2 t - 3

Anyways, thank you

Commented by JDamian last updated on 12/Jan/23

which is obviously wrong. Have you tried to get s'' and compare with a?

Answered by alcohol last updated on 12/Jan/23

a = \frac{d v}{d t} \Rightarrow v = 2 c o s (2 t) + k

k = 2 - 2 c o s (0) = 0

\Rightarrow k = 0 \Rightarrow v = 2 c o s (2 t)

v = \frac{d s}{d t} \Rightarrow s = s i n (2 t) + c

c = - 3 - s i n (0) = - 3

\Rightarrow s = s i n (2 t) - 3

Alcohol

Answered by Frix last updated on 12/Jan/23

s (t) = \int (\int a (t) d t) d t

\int (\int (- 4 \sin 2 t) d t) d t = \int (2 \cos 2 t + C_{1}) d t =

= \sin 2 t + C_{1} t + C_{2}

v (0) = 2

2 \cos 0 + C_{1} = 2 \Rightarrow C_{1} = 0

s (0) = - 3

\sin 0 + C_{2} = - 3 \Rightarrow C_{2} = - 3

\Rightarrow

s (t) = - 3 + \sin 2 t

Apple Juice

Commented by Rasheed.Sindhi last updated on 12/Jan/23

A p p r e c i a t e y o u r s e n s e o f h u m o u r!

Commented by Frix last updated on 12/Jan/23

{It}^{'} s better to laugh than to cry!

Commented by Rasheed.Sindhi last updated on 12/Jan/23

Well said sir!

Answered by a.lgnaoui last updated on 13/Jan/23

v = \int_{0}^{t} a d t = {[2 \cos 2 t + c]}_{0}^{t} = 2 \sin 2 t + v_{0} [c = v_{0}]

v = 2 \cos 2 t + 2

S = \int_{0}^{t} v d t = \sin 2 t + 2 t + s_{0}

t = 0 s_{0} = - 3

x = \sin 2 t + 2 t - 3