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Math Help - airplane

  1. #1
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    airplane

    HELLO EVERY ONE

    An airplane moves on the runway of the airport at aconstant acceleration, then it takes off after it travels 1.5 km on the runway at avelocity of 210 km/h . what is the acceleration of the airplane ? (please by integral)
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    \displaystyle \int_{t}^{t_2}a(t)dt=v(t_2)-v(t)=210

    Initial time let's say t=0. How long did it take to travel 1.5km? That will be t_2.

    We also know a(t)=k

    \displaystyle \int_{0}^{t_2}kdt=v(t_2)-v(0)=210\Rightarrow kt|_0^{t_2}=kt_2=v(t_2)-v(0)=210

    Can you assume the initial velocity is 0?
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  3. #3
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    yes, initial velocity = 0
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    \displaystyle \int_{0}^{t_2}kdt=v(t_2)-v(0)=210\Rightarrow kt|_0^{t_2}=kt_2=v(t_2)=210

    This is your integral, k is acceleration, and t_2 is the time it took for the plane to travel 1.5 km.
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  5. #5
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    Quote Originally Posted by BAHADEEN View Post
    HELLO EVERY ONE

    An airplane moves on the runway of the airport at aconstant acceleration, then it takes off after it travels 1.5 km on the runway at avelocity of 210 km/h . what is the acceleration of the airplane ? (please by integral)
    \displaystyle \Delta v = \int_0^t a \, dt

    \Delta v = at = 210 \, km/hr


    \displaystyle \Delta x = \int_0^t at \, dt

    \displaystyle \Delta x = \frac{1}{2}at^2 = 1.5 \, km

    you have two equations with two unknowns ... solve for  a. note that the units will be

    km/hr^2
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  6. #6
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    Thanks for the help, everyone! I appreciate it!
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