Solution: Distance Traveled by Car with Air Resistance

[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 traveled without fuel

 

[Andrew Mason]

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 traveled without fuel

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