airplane

**BAHADEEN** · Jan 2nd 2011, 11:59 AM

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)

**dwsmith** · Jan 2nd 2011, 12:54 PM

$\displaystyle \int_{t}^{t_2}a(t)dt=v(t_2)-v(t)=210$

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?

**BAHADEEN** · Jan 2nd 2011, 01:20 PM

yes, initial velocity = 0

**dwsmith** · Jan 2nd 2011, 01:27 PM

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

This is your integral, k is acceleration, and t_2 is the time it took for the plane to travel 1.5 km.

**skeeter** · Jan 2nd 2011, 01:35 PM

Originally Posted by BAHADEEN

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

$km/hr^2$

**BAHADEEN** · Jan 2nd 2011, 01:38 PM

Thanks for the help, everyone! I appreciate it!

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