An automobile traveling along a straight road increases its speed from 72 ft/s to 84 ft/s in 180 ft. if the acceleration is constant, how much time elapses while the auto moves the 180 ft? answer in units of s.

The equation that would allow us to calculate for the acceleration given the distance is written below,

      a = (Vf² - Vo²) / 2d

where a is the acceleration, Vf is the final velocity, Vo is the initial velocity, and d is distance. 

Substituting the known values,
    a = ((84 ft/s)² - (72 ft/s)²) / 2(180 ft) = 5.2 ft/s²

Then, the equation that would relate the initial velocity, distance, acceleration and time is calculated through the equation,
      
     d = Vot + 0.5at²

Substituting the known values,
    180 = 72(t) + 0.5(5.2)(t²)

The value of t from the equation is 2.3 s

ANSWER: 2.3 s

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