distance an object falls

Question

The distance that an object falls from rest, when air resistance is negligible, varies directly as the square of the time. A stone dropped from rest travels 144 feet in the first 3 seconds. How far does it travel in the first 4 seconds?

Answer 1

Use the relation for constant acceleration starting from rest:

 

d = (1/2)at²

 

d = distance it fell

 

a = acceleration

 

t = time

 

Since a is not given, start by finding a using the given information:

 

d = (1/2)at² ⇒ a = 2d/t² = 2(144 ft)/(3s)² = 32 ft/s²

 

d = (1/2)(32 ft/s²)t² = 16t², with t in seconds, d in feet

 

Then after 4 seconds,

 

d = 16(4)² ft = 256 ft

 

It falls 256 ft after 4 seconds.