8. han accidentally drops his water bottle from the balcony of his apartment building. the equation d = 32…
8. han accidentally drops his water bottle from the balcony of his apartment building. the equation d = 32 - 5t² gives the distance from the ground, d, in meters after t seconds. a. complete the table and plot the data on the coordinate plane. b. is the water bottle falling at a constant speed? explain how you know.
Answer
Explanation:
Step1: Substitute t = 0 into the formula
When (t = 0), (d=32 - 5\times0^{2}=32)
Step2: Substitute t = 0.5 into the formula
When (t = 0.5), (d=32-5\times(0.5)^{2}=32 - 5\times0.25=32 - 1.25 = 30.75)
Step3: Substitute t = 1 into the formula
When (t = 1), (d=32-5\times1^{2}=32 - 5=27)
Step4: Substitute t = 1.5 into the formula
When (t = 1.5), (d=32-5\times(1.5)^{2}=32-5\times2.25=32 - 11.25 = 20.75)
Step5: Substitute t = 2 into the formula
When (t = 2), (d=32-5\times2^{2}=32 - 5\times4=32 - 20 = 12)
The completed table is:
| (t) (seconds) | (d) (meters) |
|---|---|
| 0 | 32 |
| 0.5 | 30.75 |
| 1 | 27 |
| 1.5 | 20.75 |
| 2 | 12 |
For part b: The speed of the water - bottle is the rate of change of the distance with respect to time. The distance formula is (d(t)=32 - 5t^{2}). The change in distance (\Delta d) between two time - intervals is not the same for equal time intervals. For example, from (t = 0) to (t = 1), (\Delta d=32 - 27 = 5) meters. From (t = 1) to (t = 2), (\Delta d=27 - 12 = 15) meters. Since the change in distance over equal time intervals is not constant, the speed is not constant.
Answer:
a. See the completed table above. b. No, because the change in distance over equal time intervals is not constant.