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A car traveling 36 mi/h accelerates uniformly for 5.4 s, covering 595 ft in this time. What was its acceleration? Round your

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## Answers ( )

First convert from mi/h to ft/s. There are 5280 ft to 1 mi, and 3600 s to 1 h, so

36 mi/h = (36 mi/h) * (5280 ft/mi) * (1/3600 h/s) = 52.8 ft/s

Let

abe the acceleration of the car. The car’s speed at timetisv= 52.8 ft/s +atso that after 5.4 s, it attains a speed of

v= 52.8 ft/s + (5.4 s)aRecall that

v² –u² = 2a∆xwhere

uis the car’s initial velocity and ∆xis the distance it’s traveled.We have

(52.8 ft/s + (5.4 s)

a)² – (52.8 ft/s)² = 2a(595 ft)Omitting units, this equation reduces to

(52.8 + 5.4

a)² – 52.8² = 1190a==> 29.16

a² – 619.76a= 0==> 29.16

a– 619.76 = 0==> 29.16

a= 619.76==>

a≈ 21.25 ft/s²