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

`30.0\text{ seconds}`

Step-by-step 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=(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=(16)/(0.533) \\ t=30.0\text{ seconds} \end{gathered}`

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