Question

an airplane flies eastward and accelerates uniformly. at one position along its path it has a velocity of 26.9 m/s. it then flies a further distance of 46100m and its velocity is 41.1 m/s. find the airplane's acceleration and calculate how much time elapses while the airplane covers those 46100m.

i used v2-v1/t>> 41.1-26.9/46100=3.08*10^-4...is this correct? i believe its wrong...

Answer 1

you could use \[d=\frac{1}{2}at^2+v _{i}t\] Your initial velocity, \[v _{i}\], is equivalent to 26.9m/s, your d=46,100m, and your time and acceleration are unknowns. You will have \[46,100m=.5at^2+26.9m/s*t\] \[a=\frac{ \Delta v }{ t }\]Your \[ \Delta v\] is equal to the change from your initial velocity to final velocity, which you know how to do. You plug that value into your equation...\[46,000m=.5\frac{ 14.2m/s }{ t }t^2+26.9m/s*t\]
In the first part of the equation, t^2 is the same as t*t, and if you multiply t*(14.2m/s)/t, the t in the denominator and one of the t in t^2 are canceled, leaving you with:\[46,000m=.5*14.2m/s*t+26.9*t\]The only variable you have left is t, and it would help you best if you get it alone; divide both sides by t, giving you:\[\frac{ 46,000m }{ t }=.5*14.2m/s+26.9m/s\] Simplify the 2nd part of the equation to get 33m/s. \[\frac{ 46,000m }{ t}=33m/s\] Now that this has been simplified, multiply both sides by t. You will be left with \[46,000m=33m/s*t\] Then divide both sides by 33m/s. This will leave you with \[1393.94s=t\] Now that you have time, you can plug your time value into your equation \[a=\frac{ \Delta v }{ t }\]\[a=\frac{ 14.2m/s }{ 1,393.94s }\] You will be left with your answers:\[a=0.01m/s^2\]\[t=1,393.94 s\]

Answer 2

how to find the time elapses? its telling me that isn't the time