Question

given an object that just started falling. what would the distance fallen in interval of seconds 4 - 5 compare to the time interval of seconds 1 - 2.

the distances would be the same

there is not enough information to answer

it would be a smaller distance

it would be a greater distance

Explanation:

Step1: Recall free fall distance formula

The distance fallen by a freely falling object starting from rest is given by $d = \frac{1}{2}gt^2$, where $g$ is acceleration due to gravity.

Step2: Calculate distance for 1-2s interval

First find distance at $t=1$: $d_1 = \frac{1}{2}g(1)^2 = \frac{1}{2}g$.
Distance at $t=2$: $d_2 = \frac{1}{2}g(2)^2 = 2g$.
Interval distance: $\Delta d_{1-2} = d_2 - d_1 = 2g - \frac{1}{2}g = \frac{3}{2}g$.

Step3: Calculate distance for 4-5s interval

Distance at $t=4$: $d_4 = \frac{1}{2}g(4)^2 = 8g$.
Distance at $t=5$: $d_5 = \frac{1}{2}g(5)^2 = \frac{25}{2}g$.
Interval distance: $\Delta d_{4-5} = d_5 - d_4 = \frac{25}{2}g - 8g = \frac{9}{2}g$.

Step4: Compare the two intervals

$\frac{9}{2}g > \frac{3}{2}g$, so the 4-5s interval distance is greater.

Answer:

It would be a greater distance