Chapter 11.2, Problem 62E

To determine

To find:The velocity

Answer to Problem 62E

Here, the velocity at $t=2$ seconds is -64 feet/sec.

Explanation of Solution

Given:

Position function $s\left(t\right)=-16t^2+128$

The velocity of time $t=a$ seconds is $\underset{t\to a}{\lim }\frac{s\left(a\right)-s\left(t\right)}{a-t}$

Calculation:

Substituting 2 for $a$ in the given equation, the velocity (in ft/sec) at $t=2$ seconds is given by:

  $\underset{t\to 2}{\lim }\frac{-16{\left(2\right)}^2+128-\left(-16t^2+128\right)}{2-t}=\underset{t\to 2}{\lim }\frac{16t^2-64}{2-t}$

  $=\underset{t\to 2}{\lim }\frac{16\left(t^2-4\right)}{2-t}$

  $=\underset{t\to 2}{\lim }\frac{16\left(t+2\right)\left(t-2\right)}{2-t}$

  $=\underset{t\to 2}{\lim }-16\left(t+2\right)$

  $=-64$ (By direct substitution)

Conclusion:

Therefore,the velocity at $t=2$ seconds is -64 feet/sec.