Not sure if I post this in the right thread but still hope you guys can help me out with this :-)
A body moves along a horizontal line according to s=f(t)=t^3 - 9.t^2 +24t where s is the displacement ans t is the time.
1. When is s increasing and when is it decreasing?
2. When is the velocity v increasing, and when it is decreasing?
3. Find the total distance travelled in the first 5 seconds of motion.
I have no trouble with the 1st one. With the 2nd one I suppose I should use the function v= ds/dt= 3t^2 -18t +24, hence dv/dt= 6t - 18 (please correct me if I'm wrong)
But the 3rd one makes me confused as I don't see where the unit (second) comes from, and if I just apply t=5 to s=f(t), isn't it a little bit too easy?
Thank you guys
P/s: this one is in Singapore's NTU sample paper, given its fame within our region I don't think there is anything wrong with it.