Calculating Stopping Distance: 50km/h vs 150km/h Car Speeds

[janes3kids@yahoo.com]

I got this one wrong on a test and I am debating it.
A car going 50 km/h skids to a halt going 20m. If the same car is going 150km/h how far will it skid til it comes to a halt.
a)20m b) 60m c) 180m

 

[Andrew Mason]

I got this one wrong on a test and I am debating it.
A car going 50 km/h skids to a halt going 20m. If the same car is going 150km/h how far will it skid til it comes to a halt.
a)20m b) 60m c) 180m

The car does work in skidding: Work = Force*distance where Force is the kinetic friction force. Friction is a function of the normal force, which does not change. So Work is proportional to Distance of the skid.

The car's ability to do work is its kinetic energy. KE = W. Since KE = \frac{1}{2}mv^2 if you triple v, its energy goes up by a factor 3^2=9. So the distance of skid is 9 x 20 = 180 m.

AM

 

[whozum]

Don't mean to be picky but since the car is 'skidding', the tires arent moving and its static friction.

<3 AM

 

[Doc Al]

Don't mean to be picky but since the car is 'skidding', the tires arent moving and its static friction.

"skidding" implies that the tires slide against the ground (the wheels are locked), so there is slipping between the contact surfaces and kinetic friction applies. If the car stopped without skidding, then the tires would roll without slipping and static friction would apply.

 

[hemmul]

in fact it is less than 180 m due to the heigher-than-linear-order-dependence of air resistance force on velocity... how much exactly it differs depends on the car shape.