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
