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Answer :
To find the position equation for an object moving vertically at different heights and times, we can use the formula for motion with constant acceleration.
The position equation can be found by using the formula for motion with constant acceleration, which is given by s = s0 + v0t + 0.5at^2.
To find the position equation for (a), we can substitute the given values into the equation to find the values of s0, v0, and a. For example, at t = 0 s, s = 152 ft. Plugging this into the equation gives 152 = s0. Similarly, at t = 1 s, s = 98 ft, so we have 98 = s0 + v0 + 0.5a. Using the same process for t = 2 gives us a = -24 ft/s^2.
Finally, we can substitute these values into the position equation to find s = 152 + 0t - 12t^2. The position equation for (b) and (c) can be found using the same method.
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