# Which object would have the most momentum? a. a 500-pound car moving at 20 miles per hour b. a 200-pound car moving at 60 miles per hour c. a 100-pound car moving at 80 miles per hour d. a 50-pound car moving at 100 miles per hour

The equation for momentum is given by P = mv, where m is the mass in kilograms or slugs, and v is the velocity in m/s or ft/s. Before we calculate which car has the most momentum, we need all known units in their base form: a. 500 lbs = x slugs * 32 ft/s^2; 20 m/h = 20(3600sec)/(5280ft) b. 200 lbs = x slugs * 32 ft/s^2; 60 m/h = 88 ft/s (My physics teacher had us memorize this conversion factor) c. 100 lbs = x slugs * 32 ft/s^2; 80 m/h = 80(3600sec)/(5280ft) d. 50 lbs = x slugs * 32 ft/s^2; 100 m/h = 100(3600sec)/(5280ft) Solve for the amount of slugs, convert miles per hour to feet per second, plug both into the equation P = mv, and see which has the higher number. Good luck!

Momentum is directly proportional to mass and speed. When working with SI units, the interoperability of the units is all taken care of. The proportionality constant is ' 1 ', and we can simply say Momentum = (mass, in kg) x (speed, in m/s) . In other systems of units, such as the ponderous and complex 'customary' one referenced in this question, the proportionality constant isn't ' 1 ', but momentum is still directly proportional to mass and speed. So if all we need to find is the greatest momentum from a list, we can simply look for the greatest product and not worry about the units. The actual numbers won't mean much, but each product is still directly proportional to the mass and speed that are its factors, so the greatest momentum can easily be identified. a). 500 x 20 = 10,000 'pound-mph' b). 200 x 60 = 12,000 c). 100 x 80 = 8,000 d). 50 x 100 = 5,000 (b). has the greatest product, and therefore the greatest momentum. For a meaningful number, we'd still need to do some work on the units.