4. a plane traveling at 300.0 km/h attempts to land on a 500 m runway. the plane’s engines and brakes accelerate uniformly at –5.0 m/s2. will the plane be able to land safely? show all your work. include any equations used, the given and unknown. show all calculations. express numerical answers with the correct number of significant digits. remember to carry one or two extra decimal places throughout calculation. do not round until the end.

To start this doozy of a problem, let's first get all the units in terms of meters and seconds, so that our problem is nice and easy to work with.
1km/hour = 1,000 meters/ 3600 seconds = .2777m/s
The plane's coming in at 300 *.277 = 83.33 m/s

The plane is coming in hot at 83.33m/s. How long will it take to come to a complete stop, given deceleration of -5m/s?
Vf = Vi + at ,
where Vf = final velocity, Vi=intiital velocty, a=acceleration, and t equals time. Let's solve for t. We plug 0 in for Vf, since final velocity will be zero (plane's not moving)
0 = 83.33 + (-5)t               Subtract 83.33 from both sides
-83.33 = -5t                      Divide both sides by 5
t = 16.66                            
The plane needs 16.66 seconds to come to a stop. Is this enough time to avoid a fiery demise? 

We have 500 m of runway to work with. To see if we have enough space to land, let's see how far we've traveled before we come to a complete stop, meaning how far we've traveled after 16.66 seconds. 
d = vi(t) + (1/2) *a *t²           where Vi= initial velocity. Let's solve for d
d = 83.33*16.66 + (1/2)(-5)(16.66²)
d = 1388.88 + (-2.5) (277.77)
d = 1388.88 - 694.44
d= 694.44

Looks like this pilot's out of luck, because he needs 194.44 meters more runway in order to survive this landing.