# Math problem regarding kinetic motion

1. Sep 19, 2007

### danong

Sorry, i have problem in this question which comes from my textbook. I couldn't solve it and i would like someone to guide me.

(Question)
A body travels 30 metres in the sixth second of motion and 24 meters in the ninth second. Find:
i) the initial velocity (ans: 41 m/s )
ii) the retardation, assumed uniform (ans: -2 m/s/s )
iii) the time elapsing before coming to rest (ans: 20.5s)

From my thinking is that, the body is actually moving in a curve so it changes its displacement from 30 meters to 24 meters within the time [6~9] seconds,
but this problem is in charge of kinetic problem as well, as it's in the chapter 'kinetic'.
And since it's not moving in a straightline, i assume that it cannot apply the ordinary equation : S = u * t * 1/2 a*t^2;
But by only reconstructing the equation from a = dv/dt;

Plus, the retardation and initial velocity seems to be dependantly constant variable. So my guess is that, since it involves friction, i would simply guess that it's actually having altering of work as :
Sum(W) = Fn * d(Sn);
where W is the total Work,
Fn is the changing of Forces within the time interval [0,t];
dSn is the delta of distance traveled within time interval [0,t];

Daniel.

2. Sep 19, 2007

### CompuChip

From my thinking, this means that the velocity changes from 30 m/s to 24 m/s in the [6, 9] s time interval.

Also, "the retardation is assumed uniform" sounds to me like "the acceleration is constant", which means the formula
$$s(t) = s_0 + v_0 t + \tfrac12 a t^2$$
will certainly hold (it follows from solving
$$s''(t) = a$$
with the appropriate boundary conditions).

"Kinetic" basically just means "movement". E.g. "kinetic energy" is just "movement energy", in a quite literal translation.
But perhaps what is meant is, that you should solve it using energies instead of dynamic equations?

3. Sep 19, 2007

### HallsofIvy

Why do you assert "it's not moving in a straightline"? I can find no where in the problem statement that it is said it is not moving in a straight line. "Kinetic" simply means "moving"- not necessarily moving in a curve.

Assuming constant acceleration, a, (although that's not mentioned until (b)), a body will move (1/2)at2+ v0t where v0 is the initial speed. After 5 seconds, it will have gone (25/2)a+ 5v0. After 6 seconds, it will have gone (36/2)a+ 6v. During the "6th second", it will have gone (36/2)a+ 6v0- ((25/2)a+ 5v0= (11/2)a+ v0= 30. Do the same for the distances traveled in 8 and 9 minutes, setting the difference equal to 24 and you have two equations to solve for a and v0.

4. Sep 20, 2007

### danong

oh yes! i misunderstood the question by assuming it has "travelled along". Thanks everyone for the answer and detailed explanation. I got it solved. ^^