Question

Step 2 of 2: If we ignore air resistance, a falling body will fall 16/? feet in t seconds. What is the average velocity between t=3 and t=3.2?Round your answer to two decimal places if necessary.

Answer 1

Given,

Distnace covered by the falling body in t seconds, d=16t²

the total time duration Δt=3.2-2=0.2 s

The average velocity is given by the ratio of the total distance to the time duration.

Thus the average velocity of the given body over the given time interval is given by,

$\begin{gathered} v_{av}=\frac{d}{\Delta t} \\ =\frac{16(\Delta t)^2}{\Delta t} \\ =16\times\Delta t \end{gathered}$

On substituting the known values in the above equation,

$\begin{gathered} v_{av}=16\times0.2 \\ =3.2\text{ ft/s} \end{gathered}$

Thus the average velocity of the given object is in the given period is 3.2 ft/s.