Calculus problem

Question

On the surface of the moon, astronomers notice that the distance traveled by an object falling freely is proportional to the square of the time passed after the release of the object. If the object travels 3.2meters in 2 seconds, how many seconds would it take to travel 15 meters?

Answer 1

Calculus problem

On the surface of the moon, astronomers notice that the distance traveled by an object falling freely is proportional to the square of the time passed after the release of the object. If the object travels 3.2meters in 2 seconds, how many seconds would it take to travel 15 meters?

where k is the constant of proportionality.

s(t) = kt²

3.2 = k(2)²

3.2/4 = k

4/5 = k

s(t) = 4/5t²

15 = 4t²/5

75/4 = t²

t = √(75/4)

t = 5√3/2