How far did it travel in the first 2 seconds?

Question

The distance that an object falls from rest, when air is negligible, varies directly as the square of the time. A stone dropped from rest travels 400 feet in the first 5 seconds.

Thanks in advanced.

Answer 1

d = kt² would be your model for free fall.

 

 

We need to fit the proportionality constant, k, to the information given.

 

 

In 5 seconds, the object falls 400 ft, so d = 400 when t = 5.

 

 

400 = k(5²) = 25k

 

So, k = 16.

 

 

Your equation for free fall is d = 16t².

 

 

In 2 seconds, it will fall d = 16(2²) = 64 feet.