a jet lands on arunway. between the time the jet touches the ground (t=0) and wh

Question

a jet lands on arunway. between the time the jet touches the ground (t=0) and when it comes to rest. the jet has a velocity given by v(t)=40.0m/s-5.00m/s^3*t^2.

a) write down a definite integral that will give the displacement of the jet between t=1.0s and t=1.5s?

b) what is the displacement of the jet traveled between t=1.0s and t=1.5s?

c) explain what additional information would be required to determine the location of the jet at t=1.5s?

d) how far does the jet travel between t=0s and the time when it comes to rest?

Explanation / Answer

given,

v(t)=40 - 5.00 * t^2

v(t) = ds / dt

ds / dt = 40 - 5.00 * t^2

ds = (40 - 5.00 * t^2) dt

integrating the equation

definite integral that will give the displacement of the jet between t=1.0s and t=1.5s s = [40t + 1.66 * t^3 + C] from t=1.0s and t=1.5s

putting the values

s = 40 * 1.5 + 1.66 * 1.5^3 - (40 * 1 + 1.66 * 1^3)

displacement of the jet traveled between t=1.0s and t=1.5s is = 23.9425 m

we will be needing the value of displacement at t = 0 sec for determining the location of the jet at t = 1.5 sec

if jet will come to rest that is v(t) = 0

40 - 5t^2 = 0

on solving we'll get

t = 2.8284 sec

distance between t = 0sec and t = 2.8284 sec

s = 40 * 2.8284 + 1.66 * 2.8284 ^3 - (40 * 0 + 1.66 * 0^3)

s = 150.6964 m

distance jet travel between t=0s and the time when it comes to rest = 150.6964 m

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