Math problem regarding kinetic motion

In summary, a body travels 30 meters in the sixth second of motion and 24 meters in the ninth second. Using the equation s(t) = s_0 + v_0 t + \tfrac12 a t^2, we can find the initial velocity to be 41 m/s, the retardation to be -2 m/s/s, and the time elapsed before coming to rest to be 20.5 seconds. The problem involves kinetic energy and can be solved using dynamic equations or energies. It is assumed that the body is moving in a straight line and has constant acceleration.
  • #1
danong
47
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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];


Thanks in advance.
Daniel.
 
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  • #2
danong said:
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
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
[tex]s(t) = s_0 + v_0 t + \tfrac12 a t^2[/tex]
will certainly hold (it follows from solving
[tex]s''(t) = a[/tex]
with the appropriate boundary conditions).

but this problem is in charge of kinetic problem as well, as it's in the chapter 'kinetic'.
"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
danong said:
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];


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

FAQ: Math problem regarding kinetic motion

What is kinetic motion?

Kinetic motion is the motion of an object resulting from its energy of motion, also known as its kinetic energy. This type of motion can include linear, rotational, and vibrational motions.

How do you calculate kinetic energy?

Kinetic energy can be calculated using the formula KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity. The unit for kinetic energy is joules (J).

What factors affect the kinetic energy of an object?

The kinetic energy of an object is affected by its mass and velocity. The greater the mass and velocity, the higher the kinetic energy will be. Additionally, external forces such as friction can also impact the kinetic energy of an object.

How is kinetic energy related to potential energy?

Kinetic energy and potential energy are both forms of energy that an object possesses. Kinetic energy is the energy of motion, while potential energy is the energy an object has due to its position or state. The total energy of an object is the sum of its kinetic and potential energy.

Can kinetic energy be converted into other forms of energy?

Yes, kinetic energy can be converted into other forms of energy, such as thermal energy or sound energy. This process is known as energy transformation and is governed by the law of conservation of energy, which states that energy cannot be created or destroyed, only transformed.

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