Determine the position function if the velocity function is and the initial position is .

Question

Determine the position function if the velocity function is  and the initial position is  .

Quizplus · Accepted Answer

To find the position function from the velocity function, we simply integrate the velocity function with respect to time.

∫11e^(-0.2t) dt = -55e^(-0.2t) + C

To find the value of C, we use the initial position given as 11eaa88b_91a1_2933_a696_6532aed98a68_TB5869_11.

-55e^(0) + C = 11eaa88b_91a1_2933_a696_6532aed98a68_TB5869_11

C = 11eaa88b_91a1_2933_a696_6532aed98a68_TB5869_11 + 55

C = 11eaa88b_91a1_5046_a696_512113d5c60d_TB5869_11

Therefore, the position function is given by

x(t) = -55e^(-0.2t) + 11eaa88b_91a1_5046_a696_512113d5c60d_TB5869_11

Determine the Position Function If the Velocity Function Is