# How would you answer this mechanics question? [closed]

This is not a homework question, it is from a past paper which I am using to practice. The question is shown in the image below:

I really don't know much about mechanics, so I don't even know where to start with this one. Any help much appreciated.

Thanks

• Do you need help deriving the differential equation (which is more of a physics question) or solving the differential equation (which is more of a math question)? – user137731 May 17 '15 at 17:01
• Mainly struggling to derive the DE – M Smith May 17 '15 at 17:02

Well the particle will always be subject to gravity, so you've got the $-g$ term there, since we're 'pointing upwards'.

Then we're told the particle experiences a force of magnitude $mkv$ resistive to its upward motion. From Newton's second law with constant mass $F=m\frac{dv}{dt} \Rightarrow \frac{dv}{dt} = \frac{F}{m}$ so we get the second term $-kv$.

So we've done the first bit.

Now remember that $v = \frac{dx}{dt}$ which means that to get $x$ you're going to need to integrate $\frac{dv}{dt}$ twice with respect to $t$. We have the initial condition $v(0)=v_0$ too.

The differential equation you need to solve is therefore

$$\frac{d^2 x}{dt}=-g-k\frac{dx}{dt}$$

• Okay, that really helps. Thanks. – M Smith May 17 '15 at 17:12
• No problem bud. – jonbaldie May 17 '15 at 18:24