Question

In Exercises \(1 - 4 ,\) an object dropped from rest from the top of a tall building falls \(y = 16 t ^ { 2 }\) feet in the first \(t\) seconds. Find the average speed during the first 4 seconds of fall.

Short answer

The average speed during the first 4 seconds of fall is 64 feet per second.

Step-by-step solution

Understanding the formula

The formula \(y = 16 t^{2}\) is provided by the problem, where \(y\) represents the distance fallen and \(t\) represents the time taken in seconds. This equation is derived from the physics equation for distance covered under constant acceleration starting from rest, where the acceleration in this case is due to gravity.

Calculate the total distance fallen

Substitute \(t=4\) seconds into the formula \(y = 16 t ^ { 2 }\) to get the distance fallen in the first 4 seconds. Doing this we get: \(y = 16*(4^{2}) = 256\) feet.

Calculate the average speed

The average speed is defined as total distance divided by total time. Substitute \(y=256\) feet and \(t=4\) seconds into the average speed formula to get \(\frac{256}{4} = 64\) feet per second.