Question

the velocity v of a falling object is directly proportional to the time t of the fall. if, after 2 seconds, the velocity of the object is 64 feet per second, what will its velocity be after 5 seconds? the velocity of the object after 5 seconds will be

Explanation:

Step1: Find the proportionality constant

Since $v$ is directly proportional to $t$, we have $v = kt$. When $t = 2$ and $v=64$, we substitute into the equation: $64=k\times2$. Solving for $k$, we get $k=\frac{64}{2}=32$.

Step2: Calculate the velocity at $t = 5$

Now that $k = 32$, and we want to find $v$ when $t = 5$. Using the equation $v=kt$, we substitute $k = 32$ and $t = 5$ into it: $v=32\times5 = 160$.

Answer:

160