An object moving vertically is at the given heights at the specified times. Find the position equation s = 1 2 at2 + v0t + s0 for the object.

Question

An object moving vertically is at the given heights at the specified times. Find the position equation

s=1/2at² + v₀t + s₀  for the object.

At t = 1 second, s = 148 feet

At t = 2 seconds, s = 128 feet

At t = 3 seconds, s = 76 feet

Answer 1

s(1) = 148 =-a/2 + vo + ho

s(2) = 128 = -2a +2vo+ ho

s(3) = 76 = -9a/2 + 3vo +ho

3 equations, 3 unknowns

add and subtract to eliminate variables

20= 3a/2 -vo

52 = 5a/2-vo

32 = a

vo= 48-20= 28

ho= 148+16-28= 136

s(t) =-16t^2 +28t + 136

check the answer:

s(1) =-16+28+136 = 148

s(2) =-64+56+136=128

s(3) =-144+84+136= 76