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)
$\displaystyle \displaystyle \int_{t}^{t_2}a(t)dt=v(t_2)-v(t)=210$
Initial time let's say t=0. How long did it take to travel 1.5km? That will be $\displaystyle t_2$.
We also know $\displaystyle a(t)=k$
$\displaystyle \displaystyle \int_{0}^{t_2}kdt=v(t_2)-v(0)=210\Rightarrow kt|_0^{t_2}=kt_2=v(t_2)-v(0)=210$
Can you assume the initial velocity is 0?
$\displaystyle \displaystyle \Delta v = \int_0^t a \, dt$
$\displaystyle \Delta v = at = 210 \, km/hr$
$\displaystyle \displaystyle \Delta x = \int_0^t at \, dt$
$\displaystyle \displaystyle \Delta x = \frac{1}{2}at^2 = 1.5 \, km$
you have two equations with two unknowns ... solve for $\displaystyle a$. note that the units will be
$\displaystyle km/hr^2$