IXL - Relate position, velocity, speed, and acceleration using derivatives (Calculus practice)

An object travels along a straight line. The function

(

)

–

gives the object's velocity, in feet per hour, at time

hours.

Write a function that gives the object's acceleration

(

)

in feet per hour per hour.

(

)

ref_doc_title.

Learn with an example

question

An object travels along a straight line. The function

(

)

–

gives the object's velocity, in feet per hour, at time

hours.

Write a function that gives the object's acceleration

(

)

in feet per hour per hour.

(

)

key idea

Acceleration

(

)

is the rate of change of velocity

(

)

with respect to time.

(

)

′

(

)

solution

To find the object's acceleration

(

)

calculate the first derivative of its velocity

(

)

–

(

)

′

(

)

(

–

)

′

(

)

–

(

)

–

The object's acceleration, in feet per hour per hour, is

(

)

–

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Not feeling ready yet? These can help:

H.9Find derivatives using the product rule I

H.11Find derivatives using the quotient rule I

H.14Find derivatives using the chain rule I

J.3Find second derivatives of trigonometric, exponential, and logarithmic functions

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