# Resistance to motion

1. Mar 23, 2006

### Jess1986

Any got any ideas of how to go around this question? Thanks

A car of mass m is moving along a horizontal track with speed U>uc when it runs out of fuel. The retarding force due to air resistance is equal to
(i) $$\mu u^2$$ for speed u>uc
and (ii) $$\lambda u$$ for speed u<uc

By writing Newton's second law in the form

ma = mu du/dx = retarding force
where x is distance travelled.

Find the distance travelled without fuel

2. Mar 23, 2006

### Andrew Mason

Use energy. The car stops when its energy runs out.

$$\int_{u}^{0} Fdx = m\int_{u}^{0} udu = m\int_{u}^{u_c} udu + m\int_{u_c}^{0} udu$$

By inserting the expressions for u evaluate the two integrals.

AM