Can someone explain me this?

Question

A jetliner, traveling northward, is landing with a speed of 80 m/s. Once the jet touches down, it has 785 m of runway in which to reduce its speed to 5.3 m/s. Compute the average acceleration (magnitude and direction) of the plane during landing (take the positive direction to be northward).

How do I compute the average acceleration with this data?

Answer 1

Let

v₀ = 80 m/s be the initial speed at some time t₀,

v₁ = 5.3 m/s be the final speed at some time t₁,

s = 785 m be the distance over which the plane travelled between t₀ and t₁,

a (to be computed) be the plane's acceleration.

Denote

Δt = t₁ - t₀,

Δv = v₁ - v₀ = -74.7 m/s

We use the following identities

a = Δv/Δt

s = aΔt²/2

From the first equation express

Δt = Δv/a

and substitute it into the second equation

s = a(Δv/a)²/2 = Δv²/2a

From that express

a = Δv²/2s

Substituting actual numbers

a = (-74.7)²/(2×785) = 3.536 m/s²

The above is the magnitude of the acceleration.

The direction can be obtained from

a = Δv/Δt

where Δv < 0 and Δt > 0.

Therefore a = -3.536 m/s².

That is a negative acceleration in the northward direction.

In other words, it is a positive deceleration in the northward direction, or

positive acceleration in the southward direction.