An object of mass m=1.0 kg experiences a force of the following mathematical form-
F(t)=ke^(-ct) where k=6.0 N, and c=0.101/s. At time t=0, the object has a velocity of v=2.0m/s and is at the origin. Where is this object after 20 seconds?

Question

An object of mass m=1.0 kg experiences a force of the following mathematical form-
F(t)=ke^(-ct) where k=6.0 N, and c=0.101/s. At time t=0, the object has a velocity of v=2.0m/s and is at the origin. Where is this object after 20 seconds?

fifciol · Answer

Start from this equation:
$$F=m \frac{ dv }{dt }$$
Can you determine v out of it?

fifciol · Answer

$$Fdt=mdv \Rightarrow dv=\frac{ 1 }{ m }Fdt$$
integrate both sides:
$$\int\limits dv=\frac{ 1 }{m }\int\limits Fdt=\frac{ 1 }{ m }\int\limits ke^{-ct}dt$$
so 
$$v=\frac{ k }{ m }\int\limits e^{-ct}dt$$
can you solve this integral?

fifciol · Answer

@schi1 are you still there?

anonymous · Answer

where has the k-exp(ct) come from @schi1?

anonymous · Answer

umm the formula is-
$$F(x)=ke ^{-ct}$$
where e is the constant e

anonymous · Answer

and yes I did solve the integral, thank you @Fifciol

fifciol · Answer

what is the result then? Or you've already solved the problem?