### All Calculus 2 Resources

## Example Questions

### Example Question #226 : Integrals

If and , what is the original position function?

**Possible Answers:**

**Correct answer:**

Recall that the integral of the velocity function is the position function:

Now, integrate:

Now plug in your initial conditions:

Plug your C back into your position function:

### Example Question #227 : Integrals

If and , what is the original position function?

**Possible Answers:**

**Correct answer:**

Recall that the integral of velocity is the position function:

Now, integrate. Remember to raise the exponent by 1 and also put that result on the denominator:

Now plug in your initial conditions to solve for C:

Now plug your C back in to your position function:

### Example Question #228 : Integrals

If and , what is the original position function?

**Possible Answers:**

**Correct answer:**

Recall that the integral of the velocity function is the position function:

Now, integrate. Remember to raise the exponent by 1 and also put that result on the denominator:

Now, plug in your initial conditions:

Now plug your C back into your position function:

### Example Question #229 : Integrals

In the vacuum of space, a particle is initially moving at a constant speed of only 6 meters/second away from you as you watch in your space capsule stationary relative to the particle. You track the object and then observe an acceleration that varies with time as,

After travelling for 20 minutes at this speed the particle is now km away from you. How far was it from you at the instant it began accelerating?

**Possible Answers:**

**Correct answer:**

To solve the problem we first need to find the position function by successively integrating. First find the velocity function by integrating the acceleration:

The constant of integration is the initial velocity, which we are given as 6 meters-per-second. For convenience, we will omit the units in the equation.

Now we integrate the velocity function to find the position function:

The constant of integration represents the initial position when . After the particle is km, or meters, away. Using standard S.I. units (meters and seconds), solve for at seconds where .

Now solve for