Question

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.

Answer 1

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