Question

the velocity v of a falling object is directly proportional to the time t of the fall. if, after 5 seconds, the velocity of the object is 160 feet per second. what will its velocity be after 6 seconds? the velocity of the object after 6 seconds will be

Explanation:

Step1: Find the constant of proportionality

Since $v$ is directly proportional to $t$, we have $v = kt$. Given $v = 160$ when $t = 5$, we can find $k$ as $k=\frac{v}{t}=\frac{160}{5}=32$.

Step2: Calculate the velocity at $t = 6$

Substitute $k = 32$ and $t = 6$ into $v=kt$. So $v=32\times6 = 192$.

Answer:

192 feet per second