Velocity of a particle can be found by taking the derivative of the position function with respect to time. Recall that a derivative gives the rate of change of some parameter, relative to the change of some other variable. When we take the derivative of position with respect to time, we are evaluating how position changes over time; i.e velocity!

To take the derivative of the position functions

 , 

We'll need to make use of the following derivative rule(s):

Derivative of an exponential: 

Note that u may represent large functions, and not just individual variables!

Using the above properties, the velocity functions are

Velocity of a particle can be found by taking the derivative of the position function with respect to time. Recall that a derivative gives the rate of change of some parameter, relative to the change of some other variable. When we take the derivative of position with respect to time, we are evaluating how position changes over time; i.e velocity!

To take the derivative of the position function

We'll need to make use of the following derivative rule(s):

Derivative of an exponential: 

Note that u may represent large functions, and not just individual variables!

Using the above properties, the velocity function is

Velocity of a particle can be found by taking the derivative of the position function with respect to time. Recall that a derivative gives the rate of change of some parameter, relative to the change of some other variable. When we take the derivative of position with respect to time, we are evaluating how position changes over time; i.e velocity!

To take the derivative of the position function

We'll need to make use of the following derivative rule(s):

Derivative of an exponential: 

Product rule: 

Note that u and v may represent large functions, and not just individual variables!

Using the above properties, the velocity function is

Velocity of a particle can be found by taking the derivative of the position function with respect to time. Recall that a derivative gives the rate of change of some parameter, relative to the change of some other variable. When we take the derivative of position with respect to time, we are evaluating how position changes over time; i.e velocity!

To take the derivative of the position function

We'll need to make use of the following derivative rule(s):

Derivative of an exponential: 

Product rule: 

Note that u and v may represent large functions, and not just individual variables!

Using the above properties, the velocity function is

Velocity of a particle can be found by taking the derivative of the position function with respect to time. Recall that a derivative gives the rate of change of some parameter, relative to the change of some other variable. When we take the derivative of position with respect to time, we are evaluating how position changes over time; i.e velocity!

To take the derivative of the position function

We'll need to make use of the following derivative rule:

Derivative of an exponential: 

Note that u may represent large functions, and not just individual variables!

Using the above properties, the velocity function is

Velocity of a particle can be found by taking the derivative of the position function with respect to time. Recall that a derivative gives the rate of change of some parameter, relative to the change of some other variable. When we take the derivative of position with respect to time, we are evaluating how position changes over time; i.e velocity!

For the position function , the velocity function is

Velocity of a particle can be found by taking the derivative of the position function with respect to time. Recall that a derivative gives the rate of change of some parameter, relative to the change of some other variable. When we take the derivative of position with respect to time, we are evaluating how position changes over time; i.e velocity!

To take the derivative of the position function

We'll need to make use of the following derivative rule(s):

Derivative of an exponential: 

Note that u may represent large functions, and not just individual variables!

Using the above properties, the velocity function is

The particle is stationary when this velocity is zero:

Velocity of a particle can be found by taking the derivative of the position function with respect to time. Recall that a derivative gives the rate of change of some parameter, relative to the change of some other variable. When we take the derivative of position with respect to time, we are evaluating how position changes over time; i.e velocity!

To take the derivative of the position function

We'll need to make use of the following derivative rule(s):

Note that u may represent large functions, and not just individual variables!

Using the above properties, the velocity function is:

The particle is stationary when this function equals zero:

Though there are multiple roots to this equation:

However, for the time that the particle is first stationary, we'll only consider the first positive value:

Velocity of a particle can be found by taking the derivative of the position function with respect to time. Recall that a derivative gives the rate of change of some parameter, relative to the change of some other variable. When we take the derivative of position with respect to time, we are evaluating how position changes over time; i.e velocity!

To take the derivative of the position function

We'll need to make use of the following derivative rule(s):

Derivative of an exponential: 

Trigonometric derivative: 

Note that u may represent large functions, and not just individual variables!

Using the above properties, the velocity function is

To find when the particle is stationary, set this equation equal to zero:

There are multiple negative values which satisfy this equation; however, since we start at , the answer is

Velocity of a particle can be found by taking the derivative of the position function with respect to time. Recall that a derivative gives the rate of change of some parameter, relative to the change of some other variable. When we take the derivative of position with respect to time, we are evaluating how position changes over time; i.e velocity!

To take the derivative of the position function

We'll need to make use of the following derivative rule(s):

Derivative of an exponential: 

Note that u may represent large functions, and not just individual variables!

Using the above properties, the velocity function is

To find when the particle is stationary, set this value equal to zero:

The particle is first stationary at time