A particle moves along a straight line from a fixed point [math]P[/math] at time [math]t[/math] seconds. The acceleration, [math]a[/math][math]ms^{-2}[/math], of the particle at time [math]t[/math] is given by [math]a=mt+n[/math], where [math]m[/math] and [math]n[/math] are constants. The particle starts moving with an initial velocity of [math]30ms^{-1}[/math], decelerates to [math]20ms^{-1}[/math], and stops momentarily at [math]t=2[/math].[br][Assume motion is in the positive direction.]
(a) Determine the values of [math]m[/math] and [math]n[/math].
[math]m=5[/math],[br][math]n=-20[/math]
(b) Express the displacement function, [math]s[/math] for the movement of the particle in terms of [math]t[/math].
s = [math]\frac{5}{6}t^3-10t^2+30t[/math]
(c) Determine the values of [math]t[/math], in seconds, when the particle stops momentarily for the second time.
(d) Calculate the distance, in [math]m[/math], that the particle travels in seconds of 2.
[math]\frac{35}{6}m[/math]