# Mechanics and Units Problems

1. Suppose my car engine has a displacement of 350 cubic inches. I wish to compare this with a European car which has a displacement of 1.7 liters. Convert 350 cubic inches to liters.

2. Suppose an astronaut on an alien planet drops a hammer and finds that it falls a total distance of 6.0 yards in 2.0 seconds.

a. How far will the hammer fall in a total of 4.0 seconds.

b. How much time does it take the hammer to drop the first 1.5 yards. ( This is 1/4 of the distance it falls in 2.0 seconds.)

3. A bicycle rider is riding on level ground when he stops pedaling and coasts to a stop. Just before he quits pedaling, he is traveling at 9.0 m/s. It takes a time of 6.0 s for him to come to a stop. Determine how far the bike travels after the rider quits pedaling.

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#### Solution Preview

In case you are not yet acquainted with customary notations, "sqrt" means "square root", a^b means "a to the power b", "approx" means "approximately equal", etc

(1)

There are various web pages converting between inches and centimeters, as for example http://www.javascriptkit.com/script/script2/inchconvert.shtml.

The conversion is 1 Inch = 2.54 cm.

Therefore 1 cubic Inch = (2.54 cm)^3 approx 16.4 cm^3, and

350 in^3 approx 350 * 16.4 cm^3 approx 5735 cm^3

There are 1000 cm^3 in one liter, therefore 350 in^3 approx 5.735 liters

This you compare with a European car engine of displacement 1.7 liters

(2)

The formula for free fall is h = gt^2/2, where h is the height ...