Calculus 1 : Acceleration
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Example Question #31 : How To Find Acceleration
Suppose the position function of a particle can be traced by 
To find the acceleration of the particle given the position function, take the 2nd derivative of the position function using the Power Rule.
Substitute 
Example Question #32 : How To Find Acceleration
A car is driving north on a highway at a constant velocity of 
If a car is travelling north at constant velocity 60 mph, it's possible to write a velocity function for this vehicle, where 
To find the acceleration, take the derivative of the velocity function.
The acceleration after an hour, or any time 
Example Question #31 : How To Find Acceleration
The velocity of an object is given by the equation 
The acceleration of the object can be found by taking the derivative of the velocity equation.
The acceleration equation is then
Example Question #31 : How To Find Acceleration
If a car's velocity goes from 
Write the formula for average acceleration.
The initial velocity is 50 mph, and the final velocity is 20 mph.
Substitute all givens and solve for the acceleration.
Example Question #31 : How To Find Acceleration
The position of an object is describe by the function 
Acceleration cannot be negative.
To find the acceleration function, derive 
Substitute 
Example Question #32 : How To Find Acceleration
Consider the position function 
Find the function which models the acceleration of the particle.
Recall that velocity is the first derivative of position and acceleration is the second derivative of position.
So given:
Apply the power rule to each term to find the velocity.
Applying the power rule a second time we arrive at the acceleration function.
Example Question #32 : How To Find Acceleration
Consider the position function 
Find the acceleration of the particle after 
Recall that velocity is the first derivative of position and acceleration is the second derivative of position.
So given:
Find a(3) to find the acceleration after 3 seconds:
So our acceleration after three seconds is 224 units per second
Example Question #31 : How To Find Acceleration
Find the acceleration of an object at 
To find the acceleration of an object from the velocity function, simply take the derivative of the velocity function and substitute 
Take the derivative of 
Substitute the time to find acceleration.
Example Question #31 : How To Find Acceleration
The displacement of an object at time 
The acceleration is the 2nd derivative of the displacement. Knowing the equation of displacement, 
Differentiating the equation gives us the velocity,
Differentiating the equation a second time gives us the acceleration.
Therefore, the answer is 0.
Example Question #31 : How To Find Acceleration
The velocity of an object at time 
The acceleration can be found by taking the derivative of the velocity equation 
Using the power rule:
We find the acceleration equation to be
We can now find the acceleration at t=4
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