All Calculus 1 Resources
Example Questions
Example Question #91 : How To Find Velocity
What is the average velocity of an object from to if the position of the function is described by ?
Write the average velocity equation given the initial and final velocities.
Solve for .
Solve for .
Substitute the knowns into the average velocity equation.
Example Question #91 : Spatial Calculus
Find the instantaneous velocity at if the position function is described by .
Do not confuse average velocity with instantaneous velocity. To determine the instantaneous velocity, take the derivative of the position function to obtain the velocity function.
Substitute .
Example Question #92 : How To Find Velocity
For this question, keep in mind that velocity is defined as .
If a particle's position is given by the equation what is the particle's velocity at ?
Velocity can be viewed at the derivative of position, i.e. the rate of change of a position function.
So, we can find velocity by finding the derivative of the position function.
The position function is given as , so the derivative of the position function, using the power rule is,
, a constant, and the velocity function is thus always .
Example Question #94 : Calculus
The position of a marble is defined by the equation . What is the velocity of the marble at ?
By definition, velocity is the first derivative of a position function.
Therefore, .
For this particular problem we will use the power rule to find the derivative. The power rule states,
Since
, then applying the power rule we find
.
Plugging in gets us,
.
Example Question #91 : How To Find Velocity
A tortoise's position is defined by the equation . What is the velocity of the tortoise at ?
By definition, velocity is the first derivative of a position function.
Therefore, .
For this particular problem we will use the power rule to find the derivative. The power rule states,
Since , then applying the power rule we find .
Plugging in gets us .
Example Question #92 : Spatial Calculus
A speedboat's position is defined by the equation . What is the velocity of the speedboat at ?
By definition, velocity is the first derivative of a position function. Therefore, .
For this particular problem we will use the power rule to find the derivative.
The power rule states,
Since , then applying the power rule we find .
Plugging in gets us .
Example Question #92 : Spatial Calculus
What is the velocity of an object with a position function at ?
Velocity is the first derivative of position, or .
Given,
we can use the power rule which states,
.
Applying this rule we can deduce that,
.
Swapping in , we get
.
Example Question #93 : Spatial Calculus
What is the velocity of a car with a position function at ?
Velocity is the first derivative of position, or .
Given,
,
we can use the power rule which states,
.
Applying this rule we can deduce that,
.
Swapping in , we get
.
Example Question #94 : Spatial Calculus
What is the velocity of a speedboat with a position function at ?
Velocity is the first derivative of position, or .
Given,
,
we can use the power rule which states,
.
Applying the power rule we can deduce that,
.
Swapping in , we get
.
Example Question #91 : Calculus
Given a particle's position as a function of time, determine its velocity at a time of 4 seconds.
Since velocity is a rate change of position with respect to time, we need to take the derivative of the position function with respect to time:
At
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