[i]A particle moves along a straight line from a fixed point [math]O[/math]. The displacement, [math]s[/math] in meters, of the particle at time [math]t[/math] after passing [math]O[/math] is given by [math]s=t^3-3t+1[/math].[br][Assume motion to the right as positive.][/i][br][br][i](a) [/i][i]Express the velocity, [/i][math]v[/math][math]ms^{-1}[/math][i] , and acceleration, [/i][math]a[/math][math]ms^{-2}[/math][i] , in terms of [/i][math]t[/math]
[math]v=3t^2-3[/math][math]ms^{-1}[/math], [math]a=6t[/math][math]ms^{-2}[/math]
[i](b) Describe the motion of the particle when [math]t=0[/math] [/i][i] and [math]t=2[/math][/i][i].[/i]
The particle moves to the left with an initial velocity [math]-3ms^{-1}[/math] and zero acceleration. At [math]t=2[/math], the particle moves to the right with a velocity [math]9ms^{-1}[/math] and experiences an acceleration [math]12ms^{-1}[/math]
[i](c) Find the time range, in seconds, when the particle changes direction of motion.[/i][br][br]