A particle moves along the x-axis with a velocity given by for .If the particle is 5 units to the left of the origin at ,where is the particle at ?

Question

A particle moves along the x-axis with a velocity given by​  for  .If the particle is 5 units to the left of the origin at  ,where is the particle at  ? ​

Quizplus · Accepted Answer

Using the given velocity function, we can find the position function by integrating:
∫(11e^(-x))(dx) = -11e^(-x) + C

We can use the initial condition that the particle is 5 units to the left of the origin at t=0 to solve for C:
-11e^(0) + C = -5
C = -5 + 11 = 6

So the position function is:
x(t) = -11e^(-t) + 6

To find where the particle is at t=3, we plug in t=3:
x(3) = -11e^(-3) + 6 ≈ 14.8

Since this value is positive and greater than the initial position, the particle has moved to the right of the origin. We can confirm that it has moved 15 units to the right of the origin by checking the distance between the initial position and the final position:
|0 - 14.8| = 14.8

Therefore, the answer is C, 15 units to the right of the origin.

A Particle Moves Along the X-Axis with a Velocity Given