Question

How long does it take a jet to cover a distance of 900 meters while accelerating from 22 m/s to 38 m/s?

Answer 1

ANSWER

$30.0\text{ seconds}$

EXPLANATION

To find the time taken for the jet to cover the distance, we have to apply one of Newton's equations of motion to first find the acceleration:

$v^2=u^2+2as$

where v = final velocity

u = initial velocity

a = acceleration

s = distance covered

Therefore, we have that:

$\begin{gathered} 38^2=22^2+2(a)(900) \\ 1444=484+1800a \\ \Rightarrow1800a=1444-484=960 \\ a=\frac{960}{1800} \\ a=0.533m/s^2 \end{gathered}$

Now, we apply another equation of motion to find the time:

$v=u+at$

That is:

$\begin{gathered} 38=22+(0.533)t \\ 38-22=0.533t \\ 16=0.533t \\ \Rightarrow t=\frac{16}{0.533} \\ t=30.0\text{ seconds} \end{gathered}$

Therefore, it takes 30 seconds for the jet to cover the distance.