Acpw (1 Viewer)

[chewy123]

A moving particle has an acceleration a metres per second per second at time t seconds. The acceleration of the particle is given by a=2π^2 (cosπt). At time=0, the object is at the point x=0 and has a velocity v=π metres per second.

Show that the displacement, x , is given by x=-2cos(πt) + πt + 3

I keet getting x= -2cost(πt) + πt + 2
Please help

P.s. that wierd looking thing is pi

 

[lyounamu]

A moving particle has an acceleration a metres per second per second at time t seconds. The acceleration of the particle is given by a=2π^2 (cosπt). At time=0, the object is at the point x=0 and has a velocity v=π metres per second.

Show that the displacement, x , is given by x=-2cos(πt) + πt + 3

I keet getting x= -2cost(πt) + πt + 2
Please help

P.s. that wierd looking thing is pi

a = 2pi^2 cos(pi . t)
v = 2pi sin(pi . t) + c1
v = pi when t=0
i.e. pi = 2pi . sin (pi . 0) + c1
c1 = pi
Therefore, v = 2pi sin (pi . t) + pi
x = -2 cos (pi . t) +pi. t+ c2
x= 0 when t=0
i.e. 0 = -2 cos (pi . 0) + pi . 0 +c2
c2 = 2
Therefore x = -2cos(pi . t) +pi . t + 2

 

[chewy123]

So the the textbook is wrong?

 

[lyounamu]

So the the textbook is wrong?

What do you mean? My answer is the same as the answer from the textbook.

I proved that x = the textbook answer.

 

[chewy123]

test book answer is x=-2cos(πt) + πt + 3

 

[lyounamu]

test book answer is x=-2cos(πt) + πt + 3

The textbook answer must be wrong, then. If you substitute t = 0 into velocity and displacement, you will get that both are 0 which satisfy the question's requirements.