Question

I REALLY NEED HELP PLEASE!! A plane starts at rest on a straight runway. For the first 30s, the planes acceleration a is given as a function of time t by the equation a = bt^2, where b= 1/90 m/s^4 and t is in seconds. What is the planes speed at t= 30s?

Answer 1

Answer:

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Answer 2

The speed of the planes at t = 30 s is 100 m/s.

Explanation:

The acceleration of a plane is given as a function of time t as follows :

$a=bt^2$

Here,

$b=\dfrac{1}{90}$

We know that the velocity of the particle is given by :

$v=\int\limits {a{\cdot}dt}$

$v=\int\limits {bt^2{\cdot}dt}$

$v=b\int\limits {t^2{\cdot}dt}$

$v=\dfrac{bt^3}{3}$

At t = 30 seconds

$v=\dfrac{1}{90}\times \dfrac{(30)^3}{3}$

v = 100 m/s

So, the speed of the planes at t = 30 s is 100 m/s. Hence, this is the required solution.

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