# Problem: A young woman buys an inexpensive used car for stock car racing. It can attain highway speed with an acceleration of 8.40 mi/(h·s). By making changes to its engine, she can increase the net horizontal force on the car by 24.0%. With much less expense, she can remove material from the body of the car to decrease its mass by 24.0%.(a) Which of these two changes, if either, will result in the greater increase in the car’s acceleration?(b) If she makes both changes, what acceleration can she attain?

###### FREE Expert Solution

This problem asks about how the acceleration of car could be increased from 8.40 mi/h·s depending on changes to the net force applied and the car's mass.

Anytime we have a problem asking about force, mass, and acceleration (and only those quantities), we'll use Newton's 2nd Law, often written as

$\overline{){\mathbf{\sum }}{\mathbit{F}}{\mathbf{=}}{\mathbit{m}}{\mathbit{a}}}$

For some problems, we'll want it in a different form, solved for a:

$\overline{){\mathbit{a}}{\mathbf{=}}\frac{\mathbf{\sum }\mathbit{F}}{\mathbit{m}}}$

Notice that acceleration is directly proportional to net force and inversely proportional to mass.

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###### Problem Details

A young woman buys an inexpensive used car for stock car racing. It can attain highway speed with an acceleration of 8.40 mi/(h·s). By making changes to its engine, she can increase the net horizontal force on the car by 24.0%. With much less expense, she can remove material from the body of the car to decrease its mass by 24.0%.
(a) Which of these two changes, if either, will result in the greater increase in the car’s acceleration?
(b) If she makes both changes, what acceleration can she attain?