## Physics 211, Quiz 4

Question 1:

A jetliner flies north at 69 m/s. As it lands, it slows down to 6.1 m/s along a runway of length 750 m.

What is the average acceleration of the plane during the landing? Remember that acceleration is a vector...

```  Answer:   Two ways to solve this:

1) the quick way is to remember the formula

2       2
v   -  vo            =  2 * a * (x - xo)

solve for the acceleration

2           2
(69 m/s) - (6.1 m/s)     =  2 * a * (750 m)

4723 m^2 / s^2
a    =  -------------------
1500 m

=   3.1 m/s^2

which direction is it?  The plane was going due north,
and it slowed down.  So

a    =  -3.1 m/s^2  north

2) the longer way is to figure out how much time the plane
takes to land, and then use the change of velocity divided
by time to calculate acceleration

(x - xo)  =  (avg speed)       * t

6.1 m/s + 69 m/s
750 m   =  ----------------  * t
2

750 m
t   =  --------   =  20 seconds
37.6 m/s

Now, the acceleration is

6.1 m/s - 69 m/s
a   =  -----------------  = - 3.1 m/s^2
20 s

and, again, the direction is north, so

a   =  -3.1 m/s^2   north
```