1. Dynamics 2

A boy pulls a sled across ice by exerting a force of F kg wt. The mass of the sled is m kg, the friction between sled and ice is negligible but the sled is subject to air resistance in kg wt of magnitude k times the speed. If the sled starts from rest find expressions for:
i) Velocity as a function of time
and
ii) Displacement as a function of velocty

2. Originally Posted by Modernized

A boy pulls a sled across ice by exerting a force of F kg wt. The mass of the sled is m kg, the friction between sled and ice is negligible but the sled is subject to air resistance in kg wt of magnitude k times the speed. If the sled starts from rest find expressions for:
i) Velocity as a function of time
and
ii) Displacement as a function of velocty
$\displaystyle F_{net} = ma = F - kv \Rightarrow a = \frac{F - kv}{m} \Rightarrow \frac{dv}{dt} = \frac{F - kv}{m}$.

i) Solve $\displaystyle \frac{dt}{dv} = \frac{m}{F - kv}$ for v, subject to v = 0 when t = 0.

ii) Solve $\displaystyle \frac{dx}{dt} = v$ for x, subject to x = 0 when t = 0.

3. Originally Posted by Modernized