All Calculus 1 Resources
Example Questions
Example Question #321 : Acceleration
The position of is given by the following function:
Find the acceleration.
Answer not listed
In order to find the acceleration of a certain point, you first find the derivative of the position function to get the velocity function. Then find the derivative of the velocity function to get the acceleration function:
In this case, the position function is:
Then take the derivative of the position function to get the velocity function:
Then take the derivative of the velocity function to get the acceleration function:
Then, plug
into the acceleration function:
Therefore, the answer is:
Example Question #322 : Acceleration
The position of is given by the following function:
Find the acceleration.
Answer not listed
In order to find the acceleration of a certain point, you first find the derivative of the position function to get the velocity function. Then find the derivative of the velocity function to get the acceleration function:
In this case, the position function is:
Then take the derivative of the position function to get the velocity function:
Then take the derivative of the velocity function to get the acceleration function:
Then, plug into the acceleration function:
Therefore, the answer is:
Example Question #323 : Acceleration
The position of is given by the following function:
Find the acceleration.
Answer not listed
In order to find the acceleration of a certain point, you first find the derivative of the position function to get the velocity function. Then find the derivative of the velocity function to get the acceleration function:
In this case, the position function is:
Then take the derivative of the position function to get the velocity function:
Then take the derivative of the velocity function to get the acceleration function:
Then, plug into the acceleration function:
Therefore, the answer is:
Example Question #324 : Acceleration
The position of is given by the following function:
Find the acceleration.
Answer not listed
In order to find the acceleration of a certain point, you first find the derivative of the position function to get the velocity function. Then find the derivative of the velocity function to get the acceleration function:
In this case, the position function is:
Then take the derivative of the position function to get the velocity function:
Then take the derivative of the velocity function to get the acceleration function:
Then, plug into the acceleration function:
Therefore, the answer is:
Example Question #325 : Acceleration
The position of is given by the following function:
Find the acceleration.
Answer not listed
In order to find the acceleration of a certain point, you first find the derivative of the position function to get the velocity function. Then find the derivative of the velocity function to get the acceleration function:
In this case, the position function is:
Then take the derivative of the position function to get the velocity function:
Then take the derivative of the velocity function to get the acceleration function:
Then, plug into the acceleration function:
Therefore, the answer is:
Example Question #326 : Acceleration
The position of is given by the following function:
Find the acceleration.
Answer not listed
In order to find the acceleration of a certain point, you first find the derivative of the position function to get the velocity function. Then find the derivative of the velocity function to get the acceleration function:
In this case, the position function is:
Then take the derivative of the position function to get the velocity function:
Then take the derivative of the velocity function to get the acceleration function:
Then, plug into the acceleration function:
Therefore, the answer is:
Example Question #327 : Acceleration
If v(t) is a function which models the velocity of a wave as a function of time, find the function which models the wave's acceleration.
If v(t) is a function which models the velocity of a wave as a function of time, find the function which models the wave's acceleration.
We are given velocity and asked to find acceleration. To do so, we need to find the derivative of our velocity function.
Recall that the derivative of cosine is negative sine, and that the derivative of any variable can be found by multiplying the term by the exponent and reducing the exponent by one.
So we have:
Example Question #328 : Acceleration
If v(t) is a function which models the velocity of a wave as a function of time, find the the wave's acceleration when t=0.
If v(t) is a function which models the velocity of a wave as a function of time, find the the wave's acceleration when t=0.
We are given velocity and asked to find acceleration. To do so, we need to find the derivative of our velocity function.
Recall that the derivative of cosine is negative sine, and that the derivative of any variable can be found by multiplying the term by the exponent and reducing the exponent by one.
So we have:
We are not quite done yet however. We need to find a(0)
So our answer is -5
Example Question #329 : Acceleration
What is the instantaneous acceleration at time t = 25 of a particle whose positional equation is represented by s(t) = –44t2 + 70√t?
–2193
–88.82
–1328
None of the other answers
97.39
–88.82
The instantaneous acceleration is represented by the second derivative of the positional equation. Let's first calculate the velocity then the acceleration. Begin by rewriting s(t) to make the differentiation easier:
s(t) = –44t2 + 70√t = –44t2 + 70(t)1/2
v(t) = s'(t) = –88t + 70 * (1/2) * t–1/2 = –88t + 35t–1/2
a(t) = v'(t) = s''(t) = –88 - 70t–3/2 = –88 -70/(t√t)
a(5) = –88 -70/(25√25) = -88 - 70/(5 * 5) = –88 - 70/25 = –88.82
Example Question #721 : Spatial Calculus
Find the acceleration function of a particle who's velocity is given by:
To find acceleration we simply take the first derivative of velocity with respect to time:
Using the product rule:
Factoring out a .
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