Question

Without considering the effect of air resistance, the distance that an object falls

in feet is directly proportional to the square of the time
in seconds. If an object falls 64ft in 2 seconds, find the equation for
in terms of
.

Answer 1

The equation for distance fallen in terms of time can be represented as d = 16t², given that the distance is directly proportional to the square of the time.

Step-by-step explanation:

To find the equation for d in terms of t, we need to determine the constant of proportionality. Given that the distance an object falls is directly proportional to the square of the time, we can write the equation as:

d = kt²

where k is the constant of proportionality.

Using the given information that the object falls 64ft in 2 seconds, we can substitute these values into the equation:

64 = k(2)²

This simplifies to:

64 = 4k

Dividing both sides by 4 gives:

k = 16

Finally, substituting the value of k back into the equation, we have:

d = 16t²