# Calculus 1 : How to find acceleration

## Example Questions

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### Example Question #341 : How To Find Acceleration

The position of a is given by the following functions: Find the acceleration.     Explanation:

In order to find the acceleration of a certain point, you first find the derivative of the position function to get the velocity function and 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 #342 : How To Find Acceleration

Given the position function of an object in motion (in meters), find the acceleration of the object at t=2 seconds. -4.9 m/s/s

9.8 m/s/s

-9.8 m/s/s

4.9 m/s/s

-9.8 m/s/s

Explanation:

The acceleration of an object in motion at any given time is modeled by the second derivative of its position function. That is  The acceleration of the object at t=2 seconds is then In this case, the acceleration is constant across all values of t.

### Example Question #343 : How To Find Acceleration

Find the acceleration of a particle at given the following velocity function:      Explanation:

The first step is to obtain the acceleration equation.

This is done by taking the first derivative of the velocity function, using the power rule, .

The acceleration equation  can be used to find the acceleration at any given time.

In our case, plugging in 5 for t into the equation gives,  .

### Example Question #344 : How To Find Acceleration

Find the acceleration of a particle given its velocity function is .     Explanation:

The acceleration function can be found given any velocity function by taking its derivative.

Using the power rule the derivative becomes,  .

Recall that the derivative of a constant is always zero.

### Example Question #341 : How To Find Acceleration

Find the acceleration function of a car who's velocity function is given by .     Explanation:

The derivative of the velocity function is acceleration, and using the power rule ,

you get  .

Recall that the derivative of a constant is zero.

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