# Varying Force Problem

#### Xamfy19

1. 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?

2. Homework Equations
F=ma.. maybe..

3. 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.

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#### 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.