To find the velocity function of the particle, we must integrate the accleration function:

The integral was found using the following rule:

To find what C equals, we plug in the initial condition that at t=0, v=5:

Finally, replace C with the known value:

In order to find the velocity function from the position function we must derive the position function 

When taking the derivative we use the power rule which states 

Applying this rule term by term we get

As such 

In order to find the velocity function from the position function we derive the position function 

When deriving the position function we use the power rule which states

Applying this rule we get

As such

In order to find the velocity function from the position function we must derive the position function 

When taking the derivative we use the power rule which states 

Applying this rule term by term we get

As such 

To find the velocity of the truck, we must integrate the acceleration function to get the velocity function:

The integral was performed using the following rule:

Now, to solve for C, we must use the information given, that the velocity equals 2 at t=1:

Rewriting the velocity function, we get

Finally, evaluate the velocity function at t=20:

.

In order to find the velocity of a certain point, you first find the derivative of the position function to get the velocity function: 

In this case, the position function is: 

Then take the derivative of the position function to get the velocity function: 

Then, plug  into the velocity function: 

Therefore, the answer is: 

In order to find the velocity of a certain point, you first find the derivative of the position function to get the velocity function: 

In this case, the position function is: 

Then take the derivative of the position function to get the velocity function: 

Then, plug  into the velocity function: 

Therefore, the answer is: 

In order to find the velocity of a certain point, you first find the derivative of the position function to get the velocity function: 

In this case, the position function is: 

Then take the derivative of the position function to get the velocity function: 

Then, plug  into the velocity function: 

Therefore, the answer is: 

If x(t) gives the position of a particle as a function of time, find the velocity function of the particle.

Recall that velocity is the derivative of position, and acceleration is the derivative of velocity.

To find our answer, we need the derivative of x(t).

We need to recall three seperate rules to find this derivative.

First: the derivative of any polynomial can be found by multiplying by the exponent and decreasing the exponent by 1

Second: the derivative of  is 

Third: The derivative of ln(x) is equal to 

Put all that together and find our velocity function:

If x(t) gives the position of a particle as a function of time, find the velocity  of the particle after 10 seconds.

Recall that velocity is the derivative of position, and acceleration is the derivative of velocity.

To find our answer, we need the derivative of x(t).

We need to recall three seperate rules to find this derivative.

First: the derivative of any polynomial can be found by multiplying by the exponent and decreasing the exponent by 1

Second: the derivative of  is 

Third: The derivative of ln(x) is equal to 

Put all that together and find our velocity function:

Next, find v(10)

Simplify to get:

So, our answer is -21127.37