The position function x(t) of a particle moving along an x axis is [tex]x=4.00 - 6.00t^2[/tex]
a) The point at which particle stop, it's velocity = 0 m/s
So dx/dt = 0
0 = 0- 12t = -12t
So when time t= 0, velocity = 0 m/s
So the particle is starting from rest.
At t = 0 the particle is (momentarily) stop
b) When t = 0
[tex]x=4.00 - 6.00*0^2 = 4m[/tex]
SO at x = 4m the particle is (momentarily) stop
c) We have [tex]x=4.00 - 6.00t^2[/tex]
At origin x = 0
Substituting
[tex]0 = 4.00 - 6.00t^2\\ \\ t^2 = \frac{2}{3}[/tex]
t = 0.816 seconds or t = - 0.816 seconds
So when t = 0.816 seconds and t = - 0.816 seconds, particle pass through the origin.
