Question

The velocity of an object fired directly upward is given by $V=80-32t$, where $t$ is in seconds. When will the velocity be between $32$ and $64$ feet per second?

• A. The velocity will be between $32$ and $64$ feet per second between $0.8$ seconds after launch and $1.5$ seconds after launch.
• B. The velocity will be between $32$ and $64$ feet per second between $0.5$ seconds after launch and $1.5$ seconds after launch.
• C. The velocity will be between $32$ and $64$ feet per second between $0.4$ seconds after launch and $1.2$ seconds after launch.
• D. None of the above

Answer 1

The correct option is B The velocity will be between $32$ and $64$ feet per second between $0.5$ seconds after launch and $1.5$ seconds after launch.

Given, velocity of an object $V=80-32t$

Time at which velocity is $32$ feet per second is $32=80-32t$

$⟹32t=80-32⟹t=\frac{48}{32}=1.5sec$

Time at which velocity is $64$ feet per second is $64=80-32t$

$⟹32t=80-64⟹t=\frac{16}{32}=0.5sec$

Therefore, The velocity will be between $32$ and $64$ feet per second between $0.5$ seconds and $1.5$ seconds.