Minimum Constant Acceleration for Aircraft Liftoff

[delfam]

Homework Statement

aircraft has liftoff speed of 130km/hr. What minimum constant acceleration does it require if the aircraft is to be airborne after a run of 271m? answer is in m/s^2

Homework Equations

V^2 = Vi^2 + 2a(deltax)
a=(V^2)/Vi^2 + 2(deltax)

The Attempt at a Solution

(130^2)/O^2 + 2(271) = a
a = 28.79 km/hr = 230.24 m/s^2

 

[Filip Larsen]

The 2nd equation under 2) is not correct. The first equation is ok, so you just need to be careful how you isolate a from it. You should also consider what unit of the values you will use before inserting them (hint: convert km/h to m/s before inserting the value).

 

[delfam]

is this right then

(V^2) - (Vi^2)/(deltax) = 2a

 

[Filip Larsen]

Close. You may mean the right thing, but as you have written it, it misses a set of parenthesis around the the two speeds. Alternatively you can insert v_i=0 into the first equation before you start isolating for a.

 

[delfam]

so if Vi = 0 then the equation is (V^2)/(deltax) = 2a and 130km/hr = 36.11 m/s so
(36.11 m/s)^2/271m = 2a
4.812 = 2a
a = 2.41 m/s

I feel like i did it right but I need the final units in m/s^2 and isn't this in m^2/s^2

 

[Filip Larsen]

The square of velocity in unit m/s has unit m²/s² which then is divided by distance in unit m, so the resulting unit is m/s² as it should.