Write the equation for the speed of a jet plane starting its takeoff run along an airfield runway

Write the equation for the speed of a jet plane starting its takeoff run along an airfield runway if the resulting engine thrust is 90 kN and its mass is 60 tons.

Given:

F = 90 kN (kilonewton) – the resulting thrust force of the jet engine;

m = 60 tons is the mass of the aircraft.

It is required to write down the equation of the aircraft speed.

Let’s convert the units of measure of force and mass to the SI system:

F = 90 kN = 90 * 10 ^ 3 = 90,000 Newton.

m = 60 tons = 60 * 10 ^ 3 = 60,000 kilograms.

Let’s find the acceleration with which the plane is moving:

a = F / m = 90,000 / 60,000 = 9/6 = 3/2 = 1.5 m / s2.

According to the condition of the problem, the plane starts moving without initial speed. Then, the equation of the body’s velocity will have the form:

v (t) = v0 + a * t = 0 + 1.5 * t = 1.5 * t.

Answer: the equation for the airplane’s speed will be v (t) = 1.5 * t.