Set 4 Problem number 12

• Problem

• Solution 

• Generalized Solution

Problem

When an object falls freely in the vicinity of the earth's surface, the gravitational pull of the earth accelerates it at 9.8 m/s/s. How fast will a falling object, initially at rest, be moving 6.1 seconds after it begins falling?

Solution

In 6.1 seconds, an object accelerating from rest at 9.8 m/s^2 will attain a speed of 9.8 m/s/s * 6.1 seconds = 59.78 m/s.

Generalized Solution

In a constant acceleration situation, change in velocity is equal to the product of acceleration and time interval. 

• It follows that in a time interval of duration `dt an object accelerating under the influence of constant gravitational acceleration g will change its velocity by

• `dv = g `dt.

• Starting from rest the velocity attained will be equal to the change `dv.