Fariza starts running along a straight lame for 30 seconds from a starting point. Her velocity, v [math]ms^{-1}[/math], after t seconds is given by[math]v=0.9t-0.03t^2[/math] where [math]0\le t\le30[/math]. Find[br](a) the time, in seconds, when her acceleration is zero,[br](b) the distance travelled by Fariza, in metre.

[b]Solution[/b][br][br](a) Given [math]v=0.9t-0.03t^2[/math][br]Then, [math]a=\frac{dv}{dt}[/math][br] [math]a=0.9-0.06t[/math][br]When is acceleration is zero,[br] [math]a=0[/math][br][math]0.9-0.06t=0[/math][br] [math]t=15[/math][br]Hence, when [math]t=15[/math], Fariza's acceleration is zero.[br][br](b) [math]s=\int vdt[/math] When [math]t=0[/math], and [math]s=0[/math], then, [math]c=0[/math] [br]So, at time t, [math]s=0.45t^2-0.01t^3[/math],[br]When [math]t=30,s=0.45(30)^2-0.01(30)^3[/math][br] [math]s=135m[/math][br]Hence, Fariza ran a distance of [math]135m[/math] in 30 seconds.