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4 years ago

How does the velocity, the distance it has fallen and the acceleration of a free falling body change with time?

1 answer:

5 0

The acceleration a free falling body experiences due to gravity will always remain the same. It will always be -9.8 m/s^2.

Thus, the downward velocity of the body will always be increasing (or decreasing, however you want to think about it) because gravity is acting upon it.

The distance the body has fallen will increase faster and faster over time because its velocity is increasing.

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2 years ago

If you travel from Yakima to Ellensburg (Yakima to Ellensburg is 50 miles) with a speed of 60 miles/hour for half of the

koban [17]

Answer:

$\displaystyle \frac{480}{7}\approx 68.6\; \rm mph$ .

Explanation:

The average speed of an object is equal to total distance over total time.

Distance traveled: $\rm 50 \; mi$ .

How much time is taken? This trip is divided into two halves, each of distance $\displaystyle \frac{50}{2} = 25\;\rm mi$ .

Time spent on the first half of the trip:

$\displaystyle t_1 = \frac{s_1}{v_1} = \frac{25}{60} = \frac{5}{12}\; \rm hours$ .

Similarly, time spent on the second half of the trip:

$\displaystyle t_2 = \frac{s_2}{v_2} = \frac{25}{80} = \frac{5}{16}\; \rm hours$ .

In total:

$\displaystyle \frac{5}{12} + \frac{5}{16} = \frac{35}{48} \; \rm hours$ .

Average speed:

$\begin{aligned} \text{Average speed} &= \frac{\text{Total Distance}}{\text{Total Time}}\\ &= 50 \left/\frac{35}{48}\right.\\ &= 50 \cdot \frac{48}{35} \\&= \frac{480}{7}\approx 68.6\; \rm mph \end{aligned}$ .

This value turned out to be slightly different from the average of the speed during the two halves of the journey. The reason is that the object traveled at each speed for a different amount of time. It spent more time at the slower speed, which gives that speed a greater weight in the average. That explains why the average speed is closer to $\rm 60\; mph$ rather than $\rm 80\; mph$ .

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3 years ago