1. Towards the end of a 400m race, Faisal and Edward are leading and are both running at 6m/s. While Faisal is 72m from the finish line Edward is 100m from the finish line. Realising this and to beat Faisal, Edward decides to accelerate uniformly at 0.2 m/s2 until the end of the race while Faisal keeps on the same constant speed. Does Edward succeed in beating Faisal?

  no

Explanation:

Faisal will finish the race in ...

  (72 m)/(6 m/s) = 12 s

In order to beat Faisal, Edward's average speed in those 12 seconds must exceed ...

  (100 m)/(12 s) = 8 1/3 m/s

To achieve that average speed, Edward's acceleration must be ...

  (8 1/3 m/s -6 m/s)/(12 s/2) = 7/18 m/s² ≈ 0.3889 m/s²

Accelerating at only 0.2 m/s², Edward will not beat Faisal.

Additional comment

When acceleration is uniform, the average speed is reached halfway through the period of acceleration.

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day