Acceleration of a particle can be found by taking the derivative of the velocity 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 velocity with respect to time, we are evaluating how velocity changes over time; i.e acceleration! This is just like finding velocity by taking the derivative of the position function.

Taking the derivative of the function

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

Derivative of a natural log: 

Trigonometric derivative: 

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

The acceleration function is

At time 

Acceleration of a particle can be found by taking the derivative of the velocity 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 velocity with respect to time, we are evaluating how velocity changes over time; i.e acceleration! This is just like finding velocity by taking the derivative of the position function.

Taking the derivative of the function

We'll need to make use of the Product rule: 

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

Using the above properties, the velocity function is

The acceleration function is

At time 

Acceleration of a particle can be found by taking the derivative of the velocity 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 velocity with respect to time, we are evaluating how velocity changes over time; i.e acceleration! This is just like finding velocity by taking the derivative of the position function.

Taking the derivative of the function

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

Derivative of a natural log: 

Trigonometric derivative: 

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

Using the above properties, the velocity function is

The acceleration function is

At time 

Acceleration of a particle can be found by taking the derivative of the velocity 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 velocity with respect to time, we are evaluating how velocity changes over time; i.e acceleration! This is just like finding velocity by taking the derivative of the position function.

Taking the derivative of the function

The velocity function is

The acceleration function is

At time  and at all other times

Acceleration of a particle can be found by taking the derivative of the velocity 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 velocity with respect to time, we are evaluating how velocity changes over time; i.e acceleration! This is just like finding velocity by taking the derivative of the position function.

Taking the derivative of the function

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

Trigonometric derivative: 

Product rule: 

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

Using the above properties, the velocity function is

The acceleration function is

At time 

In order to find the acceleration of a certain point, you must first find the derivative of the position function which gives us the velocity function and then the derivative of the velocity function which gives us the acceleration function: 

In this case, the position function is: 

The velocity function is found by taking the derivative of the position function: 

The acceleration function is found by taking the derivative of the velocity function: 

Finally, to find the accelaration, substitute  into the acceleration function: 

Therefore, the answer is: 

In order to find the acceleration of a certain point, you must first find the derivative of the position function which gives us the velocity function and then the derivative of the velocity function which gives us the acceleration function: 

In this case, the position function is: 

The velocity function is found by taking the derivative of the position function: 

The acceleration function is found by taking the derivative of the velocity function: 

Finally, to find the accelaration, substitute  into the acceleration function: 

Therefore, the answer is: 

In order to find the acceleration of a certain point, you must first find the derivative of the position function which gives us the velocity function and then the derivative of the velocity function which gives us the acceleration function: 

In this case, the position function is: 

The velocity function is found by taking the derivative of the position function: 

The acceleration function is found by taking the derivative of the velocity function: 

Finally, to find the accelaration, substitute  into the acceleration function: 

Therefore, the answer is: 

In order to find the acceleration of a certain point, you must first find the derivative of the position function which gives us the velocity function and then the derivative of the velocity function which gives us the acceleration function: 

In this case, the position function is: 

The velocity function is found by taking the derivative of the position function: 

The acceleration function is found by taking the derivative of the velocity function: 

Finally, to find the accelaration, substitute  into the acceleration function: 

Therefore, the answer is: 

In order to find the acceleration of a certain point, you must first find the derivative of the position function which gives us the velocity function and then the derivative of the velocity function which gives us the acceleration function: 

In this case, the position function is: 

The velocity function is found by taking the derivative of the position function: 

The acceleration function is found by taking the derivative of the velocity function: 

Finally, to find the accelaration, substitute  into the acceleration function: 

Therefore, the answer is: