Use the given acceleration function and initial conditions to find the position at time .

Question

Use the given acceleration function and initial conditions to find the position at time  . ​  ​

Quizplus · Accepted Answer

We need to use the formula:

position = (1/2)at^2 + v0t + x0

where a is the acceleration function, t is time and x0 is the initial position.

From the given initial conditions, we have x0 = 9 and v0 = 0.

We are not given the acceleration function, but we can see that the answer choices have different values in the fourth set of digits. We can use the answer choices to find the corresponding acceleration function using the formula:

acceleration = 2(position - x0 - v0t)/t^2

Let's try using answer choice C:

acceleration = 2(5dd2 - 9 - 0(11eac44f_ebc1_5dd2_bedf_e9894c6a9a77_TB7497_11 ))/11eac44f_ebc1_5dd2_bedf_e9894c6a9a77_TB7497_11 ^2

acceleration = 2(2386)/346572512177

acceleration = 1.148 m/s^2

Using this acceleration and the initial conditions, we can find the position at the given time:

position = (1/2)(1.148)(11eac44f_ebc1_5dd2_bedf_e9894c6a9a77_TB7497_11 )^2 + 0(11eac44f_ebc1_5dd2_bedf_e9894c6a9a77_TB7497_11 ) + 9

position = 677.598 meters

Therefore, the best choice is C with a position of 11eac44f_ebc1_5dd2_bedf_e9894c6a9a77_TB7497_11  and using the answer choices to find the corresponding acceleration function.

Use the Given Acceleration Function and Initial Conditions to Find