Help With Physics Question...

m&ms

Hi all,

In an effort to revise some physics over our mid term, i have encountered a question which, after hours of trying to figure out, still eludes me...

The question:

A car of mass 1200 kg which is traveling at 100 km h(-1) wants to stop in a distance of 100 m to avoid a collision. If the maximum retarding force due to the brakes is 2000 N, will the car avoid a collision? What is the minimum force needed to avoid collision?

Answer in the back of the book says NO and 4630 N

Would anyone here be wiling to spare of few minutes of their holiday to show me how to work this out??

Thanks.

K well I'm not too sure about this, so don't take my word!

Find what acceleration the car would have to have to stop in 100m when travelling at 100km/h:

Rearrange formula v^2 = u^2 + 2as to a = (v^2 - u^2)/2s

Change 100km/h to m/s and you get 27.7778m/s

Sub that into above equation to get a=(0^2 - 27.7778^2)/2(100) when you solve you get -3.8580. Which means the car would have to have a negative acceleration of 3.8580m/s/s to stop in 100m.

Now use newtons equation from his second law F=ma to see what negative acceleration it would really have.

Rearrange to a=F/m; sub in 2000N and 1200Kg and you get 1.6667. Which means the car only has a negative acceleration of 1.6667m/s/s; thus it wouldn't stop in time.

Now the second part:

From the original a=(v^2 - u^2)/2s, we found that the cars acceleration would have to be 3.8580m/s/s.

Sub this in F=ma along with the mass:

F=(1200)(3.8580)

F=4629.6 or 4630N

Hope that helps!

m&ms

THANK YOU !!!!

The v2 = U2 + 2as formula completely slipped my mind..

That is exactly what i was looking for,
Thank you very much jammydodger :cool:

No problem at all!