# Velocity after t seconds with a time varying Force

• Physics lover
In summary, the conversation discusses the concept of force and friction being equal, resulting in no further acceleration and a constant velocity. However, the calculated velocity is different from the given answer, leading to confusion and a request for clarification. The conversation also explores the effect of friction on a block and how it relates to Newton's second law.
Physics lover
Homework Statement
I am writing the statement of problem here but its figure is in Attempt at a solution.
A 1kg block moving on horizontal rough surface of friction coefficient 0.6 is pushed with a force varying with time t in seconds as shown in figure.If initial velocity of block was 4.5 m/s.Find the velocity (in m/s) at t= 3 s.
Relevant Equations
F=Ma
dv/dt=a
Figure given in question-:

I first found out the time when force will be equal ro friction.After force becomes equal to friction there will be no acceleartion further,so velocity after that time will be same.I calculated the velocity by getting a relation of it with time.I got the velocity as 6m/s.But the answer given is 0 m/s.I can't get it.Please help.

Physics lover said:
so velocity after that time will be same
Meaning the friction miraculously disappears ?

BvU said:
Meaning the friction miraculously disappears ?
No i meant that after force becomes equal to friction,friction will balance force.
For eg:If force is 3 N friction will adjust itself to 3 N.

If the question had not mentioned any force pushing the block, only friction retarding it, then what would happen to the block?
It is moving at 4.5 m/s across this rough surface: does it continue moving at 4.5 m/s? does it suddenly stop dead? or what?

Physics lover said:
No i meant that after force becomes equal to friction,friction will balance force.
For eg:If force is 3 N friction will adjust itself to 3 N.
No, the friction stays the same till the block moves. If it is greater than the pushing forces the block will decelerate.

Although there's more than one way to do it, the problem's listed under "Momentum", so knowing the momentum form of Newton's second law,
$$F = \frac{dp}{dt}$$
think about how to solve for the final velocity given the push force (as a function of time) and the frictional force (a constant function of time).

## 1. How does the velocity change over time with a time-varying force?

The velocity of an object is directly proportional to the applied force and inversely proportional to its mass. Therefore, as the force changes over time, the velocity will also change accordingly.

## 2. What is the formula for calculating the velocity after t seconds with a time-varying force?

The formula for calculating velocity with a time-varying force is v = (1/m) ∫F(t) dt, where v is the velocity, m is the mass of the object, and F(t) is the force at a given time t.

## 3. Can the velocity after t seconds be negative with a time-varying force?

Yes, the velocity after t seconds can be negative if the force acting on the object is in the opposite direction of its initial velocity. In this case, the object will decelerate and its velocity will decrease over time.

## 4. How does the mass of an object affect its velocity with a time-varying force?

The mass of an object affects its velocity with a time-varying force by determining how much the object will accelerate or decelerate in response to the applied force. A heavier object will have a lower velocity compared to a lighter object if the same force is applied to both.

## 5. Can the velocity after t seconds with a time-varying force be constant?

It is possible for the velocity after t seconds to be constant with a time-varying force if the force applied to the object remains constant over time. However, if the force changes, the velocity will also change accordingly and will not remain constant.

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