Calculus 1 : Calculus
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Example Questions
Example Question #291 : Calculus
The position of a particle is given by the following function:
What is the velocity of the particle at 
In order to find the velocity of a particle at a certain point, we must first find the derivative.
To find the derivative we must use the trigonometric rules of differentiation for cosine and sine which states,
and the power rule,
Thus we get,
Then find the value of 
Therefore, the answer is:
Example Question #292 : Velocity
The position of a particle is given by the function 
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 a natural log:
Trigonometric derivative:
Using the above properties, the velocity function is
At time
Example Question #293 : Velocity
The position of a particle is given by the function 
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 a natural log:
Trigonometric derivative:
Using the above properties, the velocity function is
At time
Example Question #294 : Velocity
The position of a particle is given by the function 
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 a natural log:
Trigonometric derivative:
Using the above properties, the velocity function is
At time
Example Question #295 : Velocity
The position of a particle is given by the function 
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 a natural log:
Trigonometric derivative:
Using the above properties, the velocity function is
At time
Example Question #296 : Velocity
The position of a particle is given by the function 
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:
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
At time
Example Question #297 : Velocity
The position of a particle is given by the function 
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:
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
At time
Example Question #298 : Velocity
What is 
To find the velocity at 
Example Question #299 : Velocity
The position of a point is found by the following function:
What is the velocity at 
In order to find the velocity of any point given a position function, we must first find the derivative of the position function, 
This is the position function:
The derivative gives us the velocity function:
You can then find the velocity of a given point by substituting it in for the variable:
Therefore, the velocity at 
Example Question #300 : Velocity
The position of a point is found by the following function:
What is the velocity at 
In order to find the velocity of any point given a position function, we must first find the derivative of the position function, 
This is the position function:
The derivative gives us the velocity function: 
You can then find the velocity of a given point by substituting it in for the variable:
Therefore, the velocity at 
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