An object has a constant acceleration of 72 feet per second squared, an initial velocity of 17 feet per second, and an initial position of 10 feet. Find the position function describing the motion of this object.

these questions you are posting all basically all the same.

a = 72
v = 72t+c
when t = 0 , v = 17
17 = 0 + c,

v = 72t + 17
s = 36t^2 + 17t + k
when t = 0 , s = 10
so k = 10

s = 36t^2 + 17t + 10

42 ,ets

To find the position function, we need to integrate the acceleration function twice.

Step 1: Integrate the acceleration function to get the velocity function.
Given: acceleration (a) = 72 ft/s^2
Integrating a with respect to time (t) gives:
v = ∫ a dt = ∫ 72 dt = 72t + C1

Step 2: Use the given initial velocity to find the value of the constant C1.
Given: initial velocity (v0) = 17 ft/s
Setting t = 0 and solving for C1:
v(0) = 72(0) + C1
17 = C1
C1 = 17

So, the velocity function is:
v = 72t + 17

Step 3: Integrate the velocity function to get the position function.
Given: initial position (x0) = 10 ft
Integrating v with respect to t gives:
x = ∫ v dt = ∫ (72t + 17) dt = 36t^2 + 17t + C2

Step 4: Use the given initial position to find the value of the constant C2.
Given: initial position (x0) = 10 ft
Setting t = 0 and solving for C2:
x(0) = 36(0)^2 + 17(0) + C2
10 = C2
C2 = 10

So, the position function describing the motion of the object is:
x = 36t^2 + 17t + 10

To find the position function describing the motion of the object, we need to know the relationship between position, velocity, acceleration, and time. We can use the equations of motion to calculate the position function.

The first equation of motion relates the final velocity (v), initial velocity (u), acceleration (a), and time (t):

v = u + at

In this case, the initial velocity (u) is 17 ft/s, the acceleration (a) is 72 ft/s^2, and the initial position (s) is 10 ft. We need to find the position function, which is the relationship between the position (s) and time (t).

The second equation of motion relates the final position (s), initial position (s₀), initial velocity (u), acceleration (a), and time (t):

s = s₀ + ut + (1/2)at^2

Since we already know the initial position (s₀), we can rearrange this equation to solve for the position (s):

s = s₀ + ut + (1/2)at^2

s = 10 + 17t + (1/2)72t^2

Therefore, the position function describing the motion of the object is:

s(t) = 10 + 17t + 36t^2