help~~ (1 Viewer)

[elizabethy]

if x= sin2t+ 3

find
where the velocity is 0?
where the accelaration is zero?
when the particle comes to rest?

 

[wogboy]

Just a few facts you need to know:

x = position
t = time
v (velocity) = dx/dt
a (acceleration) = dv/dt
A particle is at rest when v=0

so if x = sin2t + 3
v = dx/dt = 2*cos2t
so when t=0, v = 2

a = dv/dt = -4*sin2t
so when a = 0, t = 0, pi/2, pi, 3*pi/2, 2*pi, ...
or you can say t = pi*n/2 for any integer n.

The particle is at rest when v=0.
so 2*cos2t = 0
so t = pi/4, 3*pi/4, 9*pi/4, ...

if you want you can find a general expression for t in terms of an integer n, but I don't think you need to worry about this in 2U.

 

[Rahul]

jus a little tip from left field, for q's that are worded(long sentences). i find it best to read it at least twice and then draw how the particle is moving(moving the ur pen around or whatever). then i set up a number line or number plane and place the value of whatever is given underneath, eg:

|------------------------|---------------------------|
t=o
v=5m/s...................v=0m/s
x=?........................x=10

like so. this way it makes it easier to sub in values and understanding the q better