A problem involving Force in terms of time?

In summary, a problem involving Force in terms of time? Homework Equations: F=6t2, I think they should be F=ma, dv/dt=a, ds/dt=v. Attempt at a Solution: F=3(2t2)=ma, so by Newton's second law, F=2t2. Integrating this, i got v=t3+C and s=t4/4. Now i thought initial velocity will be -10m/s which i put in C and V=0. So, 0=t3-10 or t=2.31 seconds. I have no clue what to do after this. I thought i'll substitute the
  • #1
kalpeshk2011
6
0
A problem involving Force in terms of time?

Homework Statement


There is a body of 3 kg which is moving to the right with a velocity of 10 m/s. A force of 6 N/s2t2 is applied on the body to the left. How much distane will the body have traveled from t=0 when its velocity is 0 m/s?


Homework Equations


I think they should be F=ma , dv/dt = a, ds/dt = v


The Attempt at a Solution


F=6t2
So by Newton's second law,
F=3(2t2)=ma
so i got a = 2t2
Integrating this, i got v=t3+C and s=t4/4
Now i thought initial velocity will be -10m/s which i put in C
and V=0
so, 0 = t3-10 or t=2.31 seconds
I have no clue what to do after this. I thought i'll substitute the value of t in the equation with s in it, but some how i don't think its correct. And i don't have any answers to check my solution. please help..
 
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  • #2


Hint:

Equation for s has to be written in a different form. With constant acceleration it is

s = V0t+.5at^2

You do not have constant acceleration.
 
  • #3


is the equation s=t4/4 + C??
 
  • #4


How about something like this

s = V0 * t + integral(a(t) * t)*dt

where a(t) is the acceleration, F(t)/m.

You have a mistake below for your time

"Integrating this, i got v=t^3"
 
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  • #5


Your equation s=t^4/4 is incorrect because your previous integration was incorrect.
 
  • #6


But all this mathematics and integration in physics often confuses me. I don't know when to use which technique of integration. Moreover, I have only done the rudiments of calculus. Is there any definite way to know when to use which technique?
 
  • #7


You can use whichever you feel the most comfortable. If you had solved for the time you could use definite integrals and avoid constants of integration.

When you integrate x^n you get (x^(n+1))/(n+1). Does this help?
 
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  • #8


And when you integrate

a*x^n you get a*(x^(n+1))/(n+1) where a is a constant. Do you see your mistake now?
 

FAQ: A problem involving Force in terms of time?

What is the formula for calculating force in terms of time?

The formula for calculating force in terms of time is F = m * a, where m is the mass of the object and a is the acceleration.

How does the time affect the force in a problem involving force in terms of time?

The time affects the force by determining the rate at which the force is applied. A longer time period results in a smaller force, while a shorter time period results in a larger force.

Can you provide an example of a problem involving force in terms of time?

One example of a problem involving force in terms of time is a car accelerating from 0 to 60 mph in 5 seconds. The force required to achieve this acceleration would depend on the mass of the car and the duration of the acceleration.

How does the direction of the force affect the time in a problem involving force in terms of time?

The direction of the force does not directly affect the time in a problem involving force in terms of time. However, the direction of the force can affect the acceleration and therefore impact the time it takes for the object to reach a certain velocity.

How can I use the concept of force in terms of time in real-world situations?

The concept of force in terms of time can be applied in various real-world situations, such as calculating the necessary force to lift an object or the force required to stop a moving object. It can also be used to analyze the impact of forces on structures and objects in engineering and construction projects.

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