# How long will it take for an object to stop with a defined force over time?

• Samwell
In summary, the conversation is about solving a physics problem that involves calculating the time it takes for an object to stop, given its initial velocity and mass. The equation F=A-Bt is used, where A and B are given values and t represents time. The conversation mentions using acceleration and solving an integral to find the time, as well as the use of a quadratic equation. The question of which root to choose in the equation is also discussed.
Samwell
Homework Statement
How long it will take to stop the object?
Relevant Equations
v=∫F/m dt + v0
s=∫v dt + s0
Hello, I have the force defined as a function of time, where F=A-Bt and A=100N, B=100Ns-1. I have to determine, how long it will take for object to stop, if t0=0s and v0=0,2ms-1 and mass of the object is m=10kg. Can somebody please help me with this, because I'm having hard time with this task.

Hi Samwell. Welcome to PF!

What have you done so far? Have you tried plotting acceleration as a function of time? What would the area under such a graph represent? How is that related to solving your problem?

AM

Samwell
Hello, no, I have tried to solve the integral for velocity, but I wasn't successful. So when I know that F=ma and therefore a=F/m, I can solve the acceleration, but I'm not sure what should be the next.

Thank you.

Ok. So what is the condition for stopping (in terms of your equation for v)? What does that tell you about what the area under the graph of acceleration vs. time (the integral) has to be equal to?

Hint: To solve the integral, after substituting for F, break it up into the sum of two integrals.

AM

Samwell
So acceleration has to be negative and grow. But I still have no clue how to get that time from it.

Am I right with that?

Samwell said:
So acceleration has to be negative and grow. But I still have no clue how to get that time from it. View attachment 243320
Am I right with that?

Yes. That's right so far. (As as aside, note that by plugging in the numbers you have technically lost sight of the units, so you have a dimensionally unbalanced equation. Perhaps not worry too much about that.)

But I still don't know how can I determine that time from my task.

Samwell said:
But I still don't know how can I determine that time from my task.

Have you ever heard of a thing called a quadratic equation?

Yes, but I don't know how to apply this for that problem.

Samwell said:
Yes, but I don't know how to apply this for that problem.

It's difficult to see the problem. Normally with a quadratic equation the approach is to solve it. Quadratic formula? Completing the square?

Samwell
Okay, I've done it thank you very much. Just wondering which root I have to choose (actually I know which one because I have the result but I probably wouldn't if I didn't have). Can you please shortly explain why it has to be the second one in this case.

Samwell said:
Okay, I've done it thank you very much. Just wondering which root I have to choose (actually I know which one because I have the result but I probably wouldn't if I didn't have). Can you please shortly explain why it has to be the second one in this case.

One root is for a time earlier than ##t_0##.

Samwell
Ok, thank you very much.

## 1. What is force as a function of time?

Force as a function of time is a mathematical representation of how force changes over time. It shows the relationship between force and time, typically in the form of a graph or equation.

## 2. How is force as a function of time calculated?

Force as a function of time can be calculated by dividing the change in force by the change in time. This gives the average rate of change of force over time.

## 3. What is the significance of studying force as a function of time?

Studying force as a function of time is important in understanding the dynamics of objects and their motion. It can help predict the behavior of objects and determine the forces acting on them.

## 4. How does force as a function of time relate to Newton's laws of motion?

Force as a function of time is directly related to Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The graph of force as a function of time can show how an object's acceleration changes over time when different forces are applied.

## 5. Can force as a function of time be negative?

Yes, force as a function of time can be negative. This indicates that the force is acting in the opposite direction as the motion of the object. For example, if an object is moving to the right and experiences a force in the negative direction, the force as a function of time would be negative.

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