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:

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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