Answer: D. X: 1, Y: 5, Z: 8
Step-by-step explanation:
Since the object is moving at a constant acceleration, we can use the formula v = at + v₀ to find the velocity at each time. Here, v₀ is the initial velocity, which is 0 at t=0. a is the acceleration, which we don't know. t is the time, which is 1, 2, and 3 in the given chart.
Plugging in the values, we have:
v = a1 + 0 = X
v = a2 + 0 = Y
v = a*3 + 0 = Z
This system of equations can be solved by finding a and then substituting it back into the equations to find X, Y, and Z.
To solve for a, we can use any two of the equations. For example, we can subtract the first equation from the second equation to get:
Y - X = a
We can then subtract the second equation from the third equation to get:
Z - Y = a
Since a is the same in both equations, we can set them equal to each other to get:
Y - X = Z - Y
Solving this equation for X gives us:
X = Z - Y
We can use this equation to find X in terms of Y and Z.
Substituting this equation into the first equation and solving for Y gives us:
Y = (Z + X)/2
Substituting this equation into the second equation and solving for Z gives us:
Z = 2Y - X
We now have three equations that relate X, Y, and Z to each other:
X = Z - Y
Y = (Z + X)/2
Z = 2Y - X
We can use these equations to find the values of X, Y, and Z that complete the chart.
The only answer choice that gives us positive values for X, Y, and Z is:
D. X: 1, Y: 5, Z: 8