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Math Help - velocity and acceleration

  1. #1
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    velocity and acceleration

    An airplane takes off after it travelled adistance of 1350 m on the runway. The airplane started from rest,moved with aconstant acceleration for 3o seconds before taking off .what was the speed at the time of take off ? ( I need to solve by integral with my greatfull)
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  2. #2
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    Hello, BAHADEEN!

    An airplane takes off after it travelled adistance of 1350 m on the runway.
    The airplane started from rest, moved with a constant acceleration
    for 30 seconds before taking off.
    What was the speed at the time of take-off?

    Let \,a be the constant acceleration (in \text{m/sec}^2)

    Then the velocity is: . v(t) \;=\;\int a\,dt \:=\:at + v_o
    . . where \,v_o is the plane's initial velocity.

    The plane started from rest, so v_o = 0.
    . . The velocity function is: . v(t) \:=\:at .[1]


    Then the position function is: . s \;=\;\int at\,dt \:=\:\frac{1}{2}at^2 + s_o
    . . where \,s_o is the plane's initial position.
    Assume that s_o = 0, we have: .  s(t) \:=\:\frac{1}{2}at^2 .[2]


    We are told that s = 1350 when t = 30.

    Substitute into [2]: . 1350 \:=\:\frac{1}{2}a(30^2) \quad\Rightarrow\quad a \:=\:3


    Substitute t = 30,\;a = 3 into [1]:

    . . v(30) \:=\:(3)(30) \:=\:90\text{ m/sec.}

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