Calculus 1 : Calculus

Study concepts, example questions & explanations for Calculus 1

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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 ?

Possible Answers:

Correct answer:

Explanation:

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 .

Possible Answers:

Correct answer:

Explanation:

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 ?

Possible Answers:

Correct answer:

Explanation:

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 ?

Possible Answers:

Correct answer:

Explanation:

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 ?

Possible Answers:

Correct answer:

Explanation:

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 ?

Possible Answers:

Correct answer:

Explanation:

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 ?

Possible Answers:

Correct answer:

Explanation:

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 ?

Possible Answers:

Correct answer:

Explanation:

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 ?

Possible Answers:

Correct answer:

Explanation:

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.

Possible Answers:

Correct answer:

Explanation:

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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