During a runway test, an aircraft starts from rest at $A$, with its displacement measured from \(A

Question

During a runway test, an aircraft starts from rest at $A$, with its displacement measured from $A$. It moves along a straight runway. Its acceleration $t$ seconds after the test begins is $a=6-0.3t\text{ m s}^{-2}$. A distance marker $B$ is $800$ metres from $A$, and the runway end $C$ is $1700$ metres from $A$. Find expressions for the velocity and displacement of the aircraft at time $t$.[3] Show that the aircraft passes $B$ at $t=20$, and find its speed then.[3] Find where the aircraft next comes to rest after starting and determine whether it stops before the end of the runway.[3]

Accepted Answer

(i) $v=6t-\dfrac3{20}t^2$, $s=3t^2-\dfrac1{20}t^3$; (ii) $60\text{ m s}^{-1}$; (iii) $1600\text{ m from }A$, which is $100\text{ m before }C$

Aircraft motion along a runway

Aircraft motion along a runway

Solution:

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