h(t) = 16t^2 - 40t + 50 represents the height, in feet, of an object above level ground at time t, in seconds. Given this information, complete the following sentence with one of the choices listed below.
At t = 1 second, the object is _________________.
Is it rising / falling and or at an increasing / decreasing rate?
rising at an increasing rate
rising at a decreasing rate
falling at an increasing rate
falling at a decreasing rate
not correctly described by any of the above
2006-10-14 06:04:04 · 5 answers · asked by chris 2 in Science & Mathematics ➔ Mathematics
The object starts at 50ft., falls to around 25ft. at about 1.25 s and then rises thereafter. Therefore, at 1s, it is still falling, but at a decreasing rate (ie. it is about to begin rising).
The first derivative is 32t - 40, so at t = 1, it is moving at a rate of -8. Negative means it is falling. The second derivative is 32. Being positive means it is accelerating upwards, which when applied to a falling object, means that it is falling at a decreasing rate.
2006-10-14 06:11:19 · answer #1 · answered by jethroelfman 3 · 0⤊ 0⤋
By investigation you will be able to see that the given expression will yield values which are increasing exponentially. In other words if you draw a graph using the given expression and using different values of t, e.g. t=1, t=2, t=3, etc., the line joining the points on the graph will be a hyperbola ( a line rising at an increasing rate).
So the answer is: the object is rising at an increasing rate.
In other words the rise is exponential. It will help to add the last word to your vocabulary.
2006-10-14 13:44:43 · answer #2 · answered by tul b 3 · 0⤊ 0⤋
The answer at t=1s is: 26
It would be rising at a increasing rate
2006-10-14 13:18:10 · answer #3 · answered by Rie 3 · 0⤊ 0⤋
falling at an increasing rate
find h(0) it comes out to be 50 so initially the height was 50 but after 1 sec its 26 so i think its a case of free fall....
2006-10-14 13:31:02 · answer #4 · answered by deez godsluv 1 · 0⤊ 0⤋
The object is falling at a decreasing rate, as shown in the chart produced by a Microsoft Works spreadsheet.
t 16t^240t h(t)
0.000.000.0050.00
0.100.164.0046.16
0.200.648.0042.64
0.301.4412.0039.44
0.402.5616.0036.56
0.504.0020.0034.00
0.605.7624.0031.76
0.707.8428.0029.84
0.8010.2432.0028.24
0.9012.9636.0026.96
1.0016.0040.0026.00
1.1019.3644.0025.36
1.2023.0448.0025.04
1.3027.0452.0025.04
1.4031.3656.0025.36
1.5036.0060.0026.00
2006-10-14 13:38:34 · answer #5 · answered by funtym888 2 · 0⤊ 0⤋