Distance after breaking work ?

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Distance after breaking work ?

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Answer 1 · 2017-03-05T19:54:54

Both cover the same distance.

Explanation:

Let $p = m_{1} v_{1} = m_{2} v_{2}$ $p = m_1 v_1 = m_2 v_2$ be the momentum attached to car and lorry.

The work needed to attain rest is in each case

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

$\frac{1}{2} m_{1} v_{1}^{2} = w_{1} = f d_{1}$ $1/2m_1v_1^2=w_1 = f d_1$ and
$\frac{1}{2} m_{2} v_{2}^{2} = w_{1} = f d_{2}$ $1/2m_2v_2^2=w_1 = f d_2$

Here $d_{1}, d_{2}$ $d_1,d_2$ are the distances covered until rest. Dividing term to term

$\frac{m_{1} v_{1}^{2}}{m_{2} v_{2}^{2}} = \frac{d_{1}}{d_{2}}$ $(m_1v_1^2)/(m_2v_2^2)=d_1/d_2$

but $m_{1} v_{1} = m_{2} v_{2}$ $m_1 v_1 = m_2 v_2$ so $\frac{d_{1}}{d_{2}} = 1$ $d_1/d_2=1$ hence $d_{1} = d_{2}$ $d_1=d_2$

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Distance after breaking work ?

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