Calculus 1 : Acceleration
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Example Questions
Example Question #111 : How To Find Acceleration
An apple rolls off of a table. It's position is given by the following: 
What is the acceleration of the apple?
Take the second derivative of 
Applying the power rule once will give us our velocity function,
Applying the power rule a second time results in our acceleration function,
Therefore, the acceleration of the apple is 
Example Question #112 : How To Find Acceleration
A boulder rolls into a valley. Its position is given by 
What is the acceleration of the boulder at 
Take the second derivative by using the Power Rule 
Applying the power rule a second time we find the acceleration function,
Example Question #113 : How To Find Acceleration
Lola tosses an acorn into the lake. The position of the acorn is represented by 
What is the acceleration of the acorn?
Take the second derivative by using the Power Rule 
Applying the power rule again we find our acceleration function,
Example Question #114 : How To Find Acceleration
Sian tosses an apple into the air. Its position is represented by 
What is the acceleration of the apple?
Take the second derivative by using the Power Rule 
Applying the power rule again we get the acceleration function,
Example Question #115 : How To Find Acceleration
Piper throws a softball. Its position is represented by 
What is the acceleration of the softball?
Take the second derivative by using the Power Rule 
Applying the power rule a second time we find the acceleration function,
Example Question #116 : How To Find Acceleration
Find the acceleration function
if
In order to find the acceleration function from the position function we need to take the second derivative of the position function.
When taking the derivative, we will use the power rule which states
and by applying this rule to each term we get
Next we find the second derivative,
Hence,
Example Question #117 : How To Find Acceleration
Find 
In order to find the acceleration function from the velocity function we need to take the derivative of the velocity function.
When taking the derivative, we will use the power rule which states
and by applying this rule to each term we get
As such,
Finally, to solve for 
Example Question #118 : How To Find Acceleration
A particle is moving according to the following equation:
What is the acceleration of the particle at the point 
The position function of the particle is given as follows:
The first derivative of the position function describes the velocity of the particle:
This derivative was found by using the power rule 
The second derivative of the function - the derivative of the first derivative of the position function - describes the acceleration of the particle:
The derivative was found by the derivative of x=1, and the derivative of the constant equaling zero.
Thus, the acceleration of the particle is 4.
Example Question #119 : How To Find Acceleration
A spaceship is traveling from Venus to Mercury according to the following equation:
Find the acceleration of the spaceship at 
None of the other answers
The acceleration of the spaceship is given by the second derivative of the position equation.
The first derivative - which describes the velocity of the spaceship - is given by
This derivative was found using the power rule This derivative was found by using the power rule
The derivative of this function (the second derivative of the initial function)- the acceleration of the spaceship - is given by
This derivative was also found using the power rule, and the rule that the derivative of a constant (in this case, 56) equals zero.
At 
Example Question #120 : How To Find Acceleration
A paper airplane flies across a room. It's position is represented by 
What is the acceleration of the airplane?
Take the first derivative by using the Power Rule (
Using the Power Rule again, find the second derivative of 
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