Sumone Help!Calculus Application (1 Viewer)

[Peek-a-boo!!!]

Howdy Mathemagicians! I need help

A moving particle has an acceleration (a) metres per second at time (t) seconds (t >0 or equal to 0).

The acceleration of the particle is given by
a=2 pi squared cos pi t.

At time t=0, the object is at the point x=0 and has a velocity v=pi metres per second.

Show that the displacement, x, is given by x=-2 cos pi t+pi t+3 for t>0 or equal to 0.
Thanks guys!

 

[SoulSearcher]

Just one question, are you sure it's x = - 2pi cos (pi*t) + pi*t + 3, because I've got the constant as 2 instead of 3.

Anyway, here's my working out.
a = 2pi² cos (pi*t)
v = int. [2pi² cos (pi*t)] dt
= 2pi sin (pi*t) + C
At t = 0, v = pi
.'. pi = 2pi sin 0 + C
.'. C = pi
.'. v = 2pi sin (pi*t) + pi
x = int. [2pi sin (pi*t) + pi)] dt
= -2cos (pi*t) + pi*t + C
At t = 0, x = 0
.'. 0 = -2cos 0 + 0 + C
0 = -2 + C
C = 2
.'. x = -2cos (pi*t) + pi*t + 2

If there's a problem there, I'll fix it up.