# Distance after breaking work ?

Mar 5, 2017

Both cover the same distance.

#### Explanation:

Let $p = {m}_{1} {v}_{1} = {m}_{2} {v}_{2}$ be the momentum attached to car and lorry.

The work needed to attain rest is in each case

The momentum $m v$ has associated a mechanical energy given by $\frac{1}{2} m {v}^{2}$. Also $f$ is the resistive force the same for both cars and $w$ is the dissipated mechanical energy, as breaking work.

$\frac{1}{2} {m}_{1} {v}_{1}^{2} = {w}_{1} = f {d}_{1}$ and
$\frac{1}{2} {m}_{2} {v}_{2}^{2} = {w}_{1} = f {d}_{2}$

Here ${d}_{1} , {d}_{2}$ are the distances covered until rest. Dividing term to term

$\frac{{m}_{1} {v}_{1}^{2}}{{m}_{2} {v}_{2}^{2}} = {d}_{1} / {d}_{2}$

but ${m}_{1} {v}_{1} = {m}_{2} {v}_{2}$ so ${d}_{1} / {d}_{2} = 1$ hence ${d}_{1} = {d}_{2}$