Finding Distance with Varying Force: A Homework Problem

[Xamfy19]

Homework Statement

An object of mass m=1.0kg experiences a force of the following mathematical form,

F(t)=k*e^(-c*t) i

where k=6.0N and c=0.10 (1/s) and i indicates the unit vector in the x-direction.At time t=0, the object has a velocity of v=2.0 m/s and is at the origin. Where is this object after 20 seconds?

Homework Equations

F=ma.. maybe..

The Attempt at a Solution

I used the force equation and F=ma to get the acceleration and was going to use the x=(vo)t +(1/2a)t^2 equation, but then I realized that doesn't make sense... I'm kind of confused though... How do you find the distance if the force varies? Thanks in advance.

 

[Dorothy Weglend]

Once you've found the acceleration, as you say, use the most general form of the equations between acceleration, velocity and displacement to find the displacement for this case.

Dorothy

 

[phucnv87]

You should use the Newton's second law in this form

$$F = m\frac{dv}{dt}$$

Then you find $$v$$ as a function of time $$t$$.

Remember that $$dx = vdt$$.

Calculate $$\int_0^{20}dx$$ to find the answer.